IB Mathematics Applications & Interpretation Question Type 2: Given an Equation of a Line, Finding the Angle of Elevation Exercises

Find the angle of inclination $\phi$ (in degrees) of the line $y=25x+9$ to the positive $x$-axis.

Find the angle of inclination $\phi$ (in degrees) of the line given by $3x-4y+12=0$ with respect to the positive $x$-axis.

Solve the equation $${\tan }^{2}x-3\tan x+2=0$$ for $x$ in $[0,\pi )$.

Simplify the expression $\frac{1-{\cos }^{2}x}{\cos x\sin x}$.

Simplify the following to an expression involving only $\tan \theta$: $$\frac{{\tan }^2\theta -{\sin }^2\theta }{{\sin }^2\theta }$$

Rearrange and simplify the equation $\sec x-\tan x=\cos x$ to an equation involving only $\sin x$.

Simplify the expression $$\frac{\tan \theta (1+\cos \theta )}{\sin \theta }$$

Prove the identity ${\tan }^2\theta +1={\sec }^2\theta$.

Calculate the acute angle (in degrees) between the lines $y=2x+1$ and $y=-\frac{1}{3}x-3$.

Express $\frac{1}{\sin x\tan x}$ in terms of $\cos x$ only.

Find the acute angle of inclination (in degrees) between the line $y=-3x+4$ and the positive $x$-axis.

Simplify the expression $\frac{\tan \theta }{\sec \theta }$ in terms of $\sin \theta$ and $\cos \theta$.

Prove the identity $$\tan x-\sin x=\frac{{\sin }^{3}x}{\cos x(1+\cos x)}.$$

Solve the equation $3\sin x-4\cos x=0$ for $x$ in the interval $[0,2\pi )$.