Given that $\tan x=\dfrac{9}{40}$ and that $\sin x$ is negative, find the exact value of each of

Question

Given that $\tan x=\dfrac{9}{40}$ and that $\sin x$ is negative, find the exact value of each of the following. $\sin x$ $\cos(-x)$ $\cot(90{}^\circ-x)$ $\operatorname{cosec}(90{}^\circ-x)$

Accepted Answer

(a) $-\frac{9}{41}$ (b) $-\frac{40}{41}$ (c) $\frac{9}{40}$ (d) $-\frac{41}{40}$

Complementary ratios from tangent with negative sine

Complementary ratios from tangent with negative sine

Solution:

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