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

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

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

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

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

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

Given $\cos x=-0.6$ and $x$ is in the third quadrant, find $\csc x$.

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

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

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

If $\sin x=\tfrac{2}{3}$ with $x$ acute, find $\tan\tfrac{x}{2}$.

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

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