Question Type 4: Finding one trigonometric value given another without finding angle Exercises

If $\tan x = \frac{4}{3}$ with $x$ acute, find $\sin x$. [2 marks]

Given $\cos x = -0.6$ and $x$ is in the third quadrant, find $\text{cosec}\,x$.

Given $\cos x=\frac{3}{4}$ where $x$ is acute, find $\sin 2x$.

Given $\sin x=\frac{4}{5}$ where $x$ is acute, find $\cos x+\cot x$.

Given $\cos x = -\frac{\sqrt{2}}{2}$ and $x$ lies in the second quadrant, find $\tan x$.

Given $\sin x = \frac{7}{25}$ where $x$ is acute, find $\cos x$.

Given $\tan x=\sqrt{3}$ and $x$ is in the third quadrant, find $\cos 2x$.

If $\sin x = \frac{2}{3}$ with $x$ acute, find the exact value of $\tan \frac{x}{2}$.

If $\sin x = 0.6$ with $x$ acute, find $\sec x$.

If $\tan x=-2$ and $x$ is in the second quadrant, find $\sin 2x$.

If $\sin x = -\frac{5}{13}$ and $x$ is in the third quadrant, find $\cos x$.

Given $\cos x = \frac{3}{5}$ where $x$ is acute, find $\sin x$.