Given that $\sec x=\dfrac{5}{2}$ and that $\sin x$ and $\cos x$ have opposite signs,

Question

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. $\cos(\pi-x)$ $\sin(-x)$ $\sec\left(\dfrac{\pi}{2}-x\right)$ $\cot\left(\dfrac{\pi}{2}-x\right)$

Accepted Answer

(a) $-\frac{2}{5}$ (b) $\frac{\sqrt{21}}{5}$ (c) $-\frac{5\sqrt{21}}{21}$ (d) $-\frac{\sqrt{21}}{2}$

Exact ratios from secant with a surd

Exact ratios from secant with a surd

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