IB Mathematics Analysis and Approaches 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 $\sin x$.