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PSLE

PSLE Foundation Mathematics

It is given that \(\sin A=-\frac{1}{\sqrt{5}}\) and \(\tan B=-\frac{3}{4}\), where \(A\) and \(B\) are in the same quadrant. Without using a calculator, find the exact value of

Given that \(\sin A=q\), where \(A\) is an obtuse angle, express \(\tan^2 A\) in terms of \(q\).

Compound and Double-Angle Identities

Symmetry of Trigonometric Functions

Exact Trigonometric Values and the Unit Circle

2025 NASS PRELIMS P1 Q6

Trigonometry

<p>It is given that&nbsp;\(\cos(7x)=\sin(2x)\). Find the value of \(x\) in degrees if&nbsp;\(7x\) is an acute angle.</p>

It is given that \(\cos(7x)=\sin(2x)\). Find the value of \(x\) in degrees if \(7x\) is an acute angle.

Trigonometric Equations

Cofunction equation with a larger multiple

<p>It is given that&nbsp;\(\cos(3x)=\sin(2x)\). Find the value of \(x\) in degrees if&nbsp;\(3x\) is an acute angle.</p>

It is given that \(\cos(3x)=\sin(2x)\). Find the value of \(x\) in degrees if \(3x\) is an acute angle.

Solving a cofunction equation with acute angles

<p>Given that&nbsp;\(\tan x=-\dfrac{20}{21}\) and that&nbsp;\(\cos x\) and \(\tan x\) have opposite signs, find the exact value of each of the following.</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">\(\sin(-x)\)</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">\(\tan(-x)\)</div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">\(\cos(90{}^\circ-x)\)</div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-paragraph">\(\cot(90{}^\circ-x)\)</div></li></ol>

Given that \(\tan x=-\dfrac{20}{21}\) and that \(\cos x\) and \(\tan x\) have opposite signs, find the exact value of each of the following.

Reciprocal Trigonometric Functions

Negative-angle and complementary ratios from tangent

<p>Given that&nbsp;\(\sec x=\dfrac{5}{2}\) and that&nbsp;\(\sin x\) and \(\cos x\) have opposite signs, find the exact value of each of the following.</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">\(\cos(\pi-x)\)</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">\(\sin(-x)\)</div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">\(\sec\left(\dfrac{\pi}{2}-x\right)\)</div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-paragraph">\(\cot\left(\dfrac{\pi}{2}-x\right)\)</div></li></ol>

Given that \(\sec x=\dfrac{5}{2}\) and that \(\sin x\) and \(\cos x\) have opposite signs, find the exact value of each of the following.

Exact ratios from secant with a surd

<p>Given that&nbsp;\(\sin x=-\dfrac{5}{13}\) and \(180{}^\circ&lt;x&lt;270{}^\circ\), find the exact value of each of the following.</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">\(\cos x\)</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">\(\tan x\)</div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">\(\operatorname{cosec} x\)</div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-paragraph">\(\cos(-x)\)</div></li></ol>

Given that \(\sin x=-\dfrac{5}{13}\) and \(180{}^\circ<x<270{}^\circ\), find the exact value of each of the following.

Exact ratios from sine in the third quadrant

<p>Given that&nbsp;\(ABC\) is a triangle and \(\tan \frac{A}{2} = \frac{1}{4}\), without using a calculator, find</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li data-list-item-id="item-1770095323419-7amj51vdw"><div class="list-item-paragraph">\(\tan A\)</div></li></ol><ol class="i-list" start="3"><li data-list-item-id="item-1770095326509-5sgbhvagg"><div class="list-item-paragraph">\(\sin (B + C)\)</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="2"><li data-list-item-id="item-1770095336350-5r6ttxh40"><div class="list-item-paragraph">\(\cos A\)</div></li></ol><ol class="i-list" start="4"><li data-list-item-id="item-1770095339425-h02q8wv7d"><div class="list-item-paragraph">\(\cos (B + C)\)</div></li></ol></div></div></div>

Given that \(ABC\) is a triangle and \(\tan \frac{A}{2} = \frac{1}{4}\), without using a calculator, find

<p>The diagram shows the graphs of \(y = a \tan bx\), where&nbsp;\(b &gt; 0\), for&nbsp;\(-3\pi &lt; x &lt; 3\pi\) and \(y = m\). The graph of \(y = a \tan bx\) passes through the point \(\left(\frac{\pi}{2}, 1\right)\) and intersects \(y = m\) at the points \(A\), \(B\) and \(C\). The coordinates of \(C\) is \((p, m)\).</p>
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" 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<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">Find the period of \(y\) and the values of \(a\) and \(b\).</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">State the coordinates of one possible point about which the graph of \(y = a \tan bx\) is symmetrical and the order of rotational symmetry.</div></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">Find, in terms of \(p\) and \(m\), the coordinates of \(A\) and \(B\).</div></li><li data-list-item-id="item-iv" data-list-item-path="item-iv"><div class="list-item-paragraph">By sketching a proper straight line on the same diagram, find the number of solutions to the equation \(k\left(x - \frac{\pi}{2}\right) + 1 - a \tan bx = 0\), where&nbsp;\(k \le 0\), for&nbsp;\(-3\pi &lt; x &lt; 3\pi\).</div></li></ol>

The diagram shows the graphs of \(y = a \tan bx\), where \(b > 0\), for \(-3\pi < x < 3\pi\) and \(y = m\). The graph of \(y = a \tan bx\) passes through the point \(\left(\frac{\pi}{2}, 1\right)\) and intersects \(y = m\) at the points \(A\), \(B\) and \(C\). The coordinates of \(C\) is \((p, m)\).

Find the period of \(y\) and the values of \(a\) and \(b\).

State the coordinates of one possible point about which the graph of \(y = a \tan bx\) is symmetrical and the order of rotational symmetry.

Find, in terms of \(p\) and \(m\), the coordinates of \(A\) and \(B\).

By sketching a proper straight line on the same diagram, find the number of solutions to the equation \(k\left(x - \frac{\pi}{2}\right) + 1 - a \tan bx = 0\), where \(k \le 0\), for \(-3\pi < x < 3\pi\).

Trigonometric Graphs and Parameters

<p>It is given that&nbsp;\(\cos \frac{9\pi}{8} = -\frac{m}{n}\). Express each of the following in terms of \(m\) and \(n\).</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">\(\cos \frac{9\pi}{8} + \cos \frac{5\pi}{4} + \cos \frac{11\pi}{8}\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(\sin \frac{9\pi}{8} + \sin \frac{5\pi}{4} + \sin \frac{11\pi}{8}\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(\cot\left(-\frac{\pi}{8}\right) + \cot\left(-\frac{\pi}{4}\right) + \cot\left(-\frac{3\pi}{8}\right)\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(\text{cosec}\hspace{0.5em} \frac{17\pi}{8} + \text{cosec}\hspace{0.5em} \frac{9\pi}{4} + \text{cosec}\hspace{0.5em} \frac{19\pi}{8}\)</span></div></li></ol>

It is given that \(\cos \frac{9\pi}{8} = -\frac{m}{n}\). Express each of the following in terms of \(m\) and \(n\).

\(\cos \frac{9\pi}{8} + \cos \frac{5\pi}{4} + \cos \frac{11\pi}{8}\)

\(\sin \frac{9\pi}{8} + \sin \frac{5\pi}{4} + \sin \frac{11\pi}{8}\)

\(\cot\left(-\frac{\pi}{8}\right) + \cot\left(-\frac{\pi}{4}\right) + \cot\left(-\frac{3\pi}{8}\right)\)

\(\text{cosec } \frac{17\pi}{8} + \text{cosec } \frac{9\pi}{4} + \text{cosec } \frac{19\pi}{8}\)

<p>It is given that&nbsp;\(\sin 25^\circ = \frac{a}{b}\). Express each of the following in terms of \(a\) and \(b\).</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">\(\sin 25^\circ + \sin 45^\circ + \sin 65^\circ\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(\cos 25^\circ + \cos 45^\circ + \cos 65^\circ\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(\tan 205^\circ + \tan 225^\circ + \tan 245^\circ\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(\sec (-25^\circ) + \sec (-45^\circ) + \sec (-65^\circ)\)</span></div></li></ol>

It is given that \(\sin 25^\circ = \frac{a}{b}\). Express each of the following in terms of \(a\) and \(b\).

\(\sin 25^\circ + \sin 45^\circ + \sin 65^\circ\)

\(\cos 25^\circ + \cos 45^\circ + \cos 65^\circ\)

\(\tan 205^\circ + \tan 225^\circ + \tan 245^\circ\)

\(\sec (-25^\circ) + \sec (-45^\circ) + \sec (-65^\circ)\)

<p>Given that&nbsp;\(\cot \gamma = -q\) and \(\frac{3 \pi}{2} &lt; \gamma &lt; 2 \pi\), express each of the following in terms of \(q\).</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: center;"><ol class="i-list"><li><div class="list-item-paragraph">\(\sin \gamma\)</div></li></ol><ol class="i-list" start="3"><li><div class="list-item-paragraph">\(\cot (\pi - \gamma)\)</div></li></ol><ol class="i-list" start="5"><li><div class="list-item-paragraph">\(\sec (-\gamma)\)</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="2"><li><div class="list-item-paragraph">\(\cos \left(\frac{\pi}{2} - \gamma\right)\)</div></li></ol><ol class="i-list" start="4"><li><div class="list-item-paragraph">\(\tan (\pi + \gamma)\)</div></li></ol><ol class="i-list" start="6"><li><div class="list-item-paragraph">\(\operatorname{cosec} \left(\frac{\pi}{2} - \gamma\right)\)</div></li></ol></div></div></div>

Given that \(\cot \gamma = -q\) and \(\frac{3 \pi}{2} < \gamma < 2 \pi\), express each of the following in terms of \(q\).

<p>Given that&nbsp;\(\tan \beta = p\) and \(180^\circ &lt; \beta &lt; 270^\circ\), express each of the following in terms of \(p\).</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li><div class="list-item-paragraph">\(\cot \beta\)</div></li></ol><ol class="i-list" start="3"><li><div class="list-item-paragraph">\(\sin (-\beta)\)</div></li></ol><ol class="i-list" start="5"><li><div class="list-item-paragraph">\(\sec (270^\circ - \beta)\)</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="2"><li><div class="list-item-paragraph">\(\sin (90^\circ - \beta)\)</div></li></ol><ol class="i-list" start="4"><li><div class="list-item-paragraph">\(\sec (\beta + 180^\circ)\)</div></li></ol><ol class="i-list" start="6"><li><div class="list-item-paragraph">\(\operatorname{cosec} (\beta - 90^\circ)\)</div></li></ol></div></div></div>

Given that \(\tan \beta = p\) and \(180^\circ < \beta < 270^\circ\), express each of the following in terms of \(p\).

<p>Given that&nbsp;\(\sec \theta = -y\) and \(\frac{\pi}{2} &lt; \theta &lt; \pi\), express each of the following in terms of \(y\).</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: center;"><ol class="i-list"><li><div class="list-item-paragraph">\(\cos \theta\)</div></li></ol><ol class="i-list" start="3"><li><div class="list-item-paragraph">\(\tan(-\theta)\)</div></li></ol><ol class="i-list" start="5"><li><div class="list-item-paragraph">\(\sec(\pi + \theta)\)</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="2"><li><div class="list-item-paragraph">\(\sin(\theta - \pi)\)</div></li></ol><ol class="i-list" start="4"><li><div class="list-item-paragraph">\(\cot \left( \frac{\pi}{2} - \theta \right)\)</div></li></ol><ol class="i-list" start="6"><li><div class="list-item-paragraph">\(\text{cosec} \left( \theta - \frac{\pi}{2} \right)\)</div></li></ol></div></div></div>

Given that \(\sec \theta = -y\) and \(\frac{\pi}{2} < \theta < \pi\), express each of the following in terms of \(y\).

<p>Given that&nbsp;\(\operatorname{cosec} \alpha = x\) and \(0^\circ &lt; \alpha &lt; 90^\circ\), express each of the following in terms of \(x\).</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li><div class="list-item-paragraph">\(\sin \alpha\)</div></li></ol><ol class="i-list" start="3"><li><div class="list-item-paragraph">\(\tan (2\pi - \alpha)\)</div></li></ol><ol class="i-list" start="5"><li><div class="list-item-paragraph">\(\sec (\alpha - 90^\circ)\)</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="2"><li><div class="list-item-paragraph">\(\cos (-\alpha)\)</div></li></ol><ol class="i-list" start="4"><li><div class="list-item-paragraph">\(\cot (90^\circ - \alpha)\)</div></li></ol><ol class="i-list" start="6"><li><div class="list-item-paragraph">\(\operatorname{cosec} (\pi - \alpha)\)</div></li></ol></div></div></div>

Given that \(\operatorname{cosec} \alpha = x\) and \(0^\circ < \alpha < 90^\circ\), express each of the following in terms of \(x\).

<p>Given that&nbsp;\(A\) and \(B\) are angles between \(\pi\) and \(2\pi\) such that&nbsp;\(\cot A = \frac{4}{3}\) and \(\sec B = \frac{5}{3}\), find the value of each of the following without using a calculator.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li><div class="list-item-paragraph">\(\sin A\)</div></li></ol><ol class="i-list" start="3"><li><div class="list-item-paragraph">\(\tan B\)</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="2"><li><div class="list-item-paragraph">\(\sec(A - 180^\circ)\)</div></li></ol><ol class="i-list" start="4"><li><div class="list-item-paragraph">\(\operatorname{cosec}\left( B-{{90}^{\circ }} \right)\)</div></li></ol></div></div></div>

Given that \(A\) and \(B\) are angles between \(\pi\) and \(2\pi\) such that \(\cot A = \frac{4}{3}\) and \(\sec B = \frac{5}{3}\), find the value of each of the following without using a calculator.

<p>Given that&nbsp;\(A\) and \(B\) are angles in the same quadrant such that&nbsp;\(\sin A = \frac{12}{13}\) and \(\cos B = -\frac{12}{13}\), find the value of each of the following without using a calculator.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li><div class="list-item-paragraph">\(\cos A\)</div></li></ol><ol class="i-list" start="3"><li><div class="list-item-paragraph">\(\sin B\)</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="2"><li><div class="list-item-paragraph">\(\operatorname{cosec}\left( {{90}^{\circ }}-A \right)\)</div></li></ol><ol class="i-list" start="4"><li><div class="list-item-paragraph">\(\tan(B + 180^\circ)\)</div></li></ol></div></div></div>

Given that \(A\) and \(B\) are angles in the same quadrant such that \(\sin A = \frac{12}{13}\) and \(\cos B = -\frac{12}{13}\), find the value of each of the following without using a calculator.

<p>Given that&nbsp;\(\tan \theta = 3\) and \(\sec \theta &lt; 0\), find the value of each of the following without using a calculator.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: center;"><ol class="i-list"><li><div class="list-item-paragraph">\(\sin \theta\)</div></li></ol><ol class="i-list" start="3"><li><div class="list-item-paragraph">\(\tan(-\theta)\)</div></li></ol><ol class="i-list" start="5"><li><div class="list-item-paragraph">\(\sec \theta\)</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="2"><li><div class="list-item-paragraph">\(\cos \theta\)</div></li></ol><ol class="i-list" start="4"><li><div class="list-item-paragraph">\(\tan \left( \frac{\pi}{2} - \theta \right)\)</div></li></ol><ol class="i-list" start="6"><li><div class="list-item-paragraph">\(\operatorname{cosec} \theta\)</div></li></ol></div></div></div>

Given that \(\tan \theta = 3\) and \(\sec \theta < 0\), find the value of each of the following without using a calculator.

<p>Given that&nbsp;\(\sin \beta = -\frac{3}{4}\) and \(\cos \beta &gt; 0\), find the value of each of the following without using a calculator.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: center;"><ol class="i-list"><li><div class="list-item-paragraph">\(\cos \beta\)</div></li></ol><ol class="i-list" start="3"><li><div class="list-item-paragraph">\(\sin(-\beta)\)</div></li></ol><ol class="i-list" start="5"><li><div class="list-item-paragraph">\(\sec \beta\)</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="2"><li><div class="list-item-paragraph">\(\tan \beta\)</div></li></ol><ol class="i-list" start="4"><li><div class="list-item-paragraph">\(\sin\left(\frac{\pi}{2} - \beta\right)\)</div></li></ol><ol class="i-list" start="6"><li><div class="list-item-paragraph">\(\mathrm{cosec} \, \beta\)</div></li></ol></div></div></div>

Given that \(\sin \beta = -\frac{3}{4}\) and \(\cos \beta > 0\), find the value of each of the following without using a calculator.

<p>Given that&nbsp;\(\cos 50^{\circ} = a\), express each of the following in terms of \(a\).</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li><div class="list-item-paragraph">\(\sin 50^{\circ}\)</div></li></ol><ol class="i-list" start="3"><li><div class="list-item-paragraph">\(\cos (-40^{\circ})\)</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="2"><li><div class="list-item-paragraph">\(\tan 130^{\circ}\)</div></li></ol><ol class="i-list" start="4"><li><div class="list-item-paragraph">\(\sin 230^{\circ}\)</div></li></ol></div></div></div>

Given that \(\cos 50^{\circ} = a\), express each of the following in terms of \(a\).

<p>Express \(\sin \theta\), \(\cos \theta\) and \(\tan \theta\) for each of the following in terms of the ratios of its basic angles.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li data-list-item-id="item-1770027902253-z0y1mtbnu"><div class="list-item-paragraph">\(\theta = -327^\circ\)</div></li></ol><ol class="i-list" start="3"><li data-list-item-id="item-1770027905020-cdb11an1p"><div class="list-item-paragraph">\(\theta = 1\frac{3}{7} \pi\)</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="2"><li data-list-item-id="item-1770027924895-fmim7vlhb"><div class="list-item-paragraph">\(\theta = 182^\circ\)</div></li></ol><ol class="i-list" start="4"><li data-list-item-id="item-1770027927221-wg1opkwxj"><div class="list-item-paragraph">\(\theta = -\frac{13}{4} \pi\)</div></li></ol></div></div></div>

Express \(\sin \theta\), \(\cos \theta\) and \(\tan \theta\) for each of the following in terms of the ratios of its basic angles.

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