Use the trigonometric identities to find functions, given $\cos x = 3/5$ and $x$ in quadrant $IV$.

Question

Use the trigonometric identities to find $\sin x$, $\tan x,$ and $\cot (-x)$, given $\cos x = 3/5$ and $x$ in quadrant IV.

Answer 1

Hint: Make use of $\sin^2x+\cos^2x=1$, $\tan x=\frac{\sin x}{\cos x}$, $\cot x = \frac{\cos x}{\sin x}$, $\cot(-x)=-\cot x$. You need the quadrant to determine the sign of $\sin x$.

Answer 2

Using All Sin Tan Cos formula, $\tan x<0$ and $\sin x<0$ as $x$ lies in the Fourth Quadrant.

Now, $\sec x=\frac1{\cos x}=\frac53$

$$\text{ So, }\tan x=-\sqrt{\sec^2x-1}$$

$$\sin x=\cos x\cdot\tan x\text{ or } =-\sqrt{1-\cos^2x}$$

$$\cot(-x)=-\cot x=-\frac1{\tan x}$$