Trigonometric Equations and Applications Online Quiz Questions

True or false: The equation $\sin^2\theta+\cos^2\theta=1$ is a trigonometric identity because it is true for every $\theta$ for which both sides are defined.

Which interval is the principal-value range of $y=\cos^{-1}x$?

What is the smaller solution, in radians, to $\tan x=1$ on $[0,2\pi)$? Round to four decimal places; answers within $0.0001$ radians are accepted.

Solve $2\sin x=\sqrt3$ on $[0,2\pi)$. Which pair lists all solutions?

True or false: Given SSA information in an oblique triangle, the Law of Sines can produce two possible triangles, so every supplementary-angle possibility must be checked against the angle-sum condition.

Which law should be used first to find the third side when two sides and their included angle are known in an oblique triangle?

Select all correct quotient identities. There is more than one correct choice.

What is the period, in radians, of the model $y=4\cos(3x-\frac{\pi}{2})+7$?

Which steps are valid parts of a general strategy for solving a trigonometric equation? Select all correct choices.

Verify the identity $\frac{1-\cos^2\theta}{\sin\theta}=\sin\theta$. Show a connected sequence of equivalent expressions and state any domain restriction.

An oblique triangle has $A=42^\circ$ and $B=71^\circ$. What is angle $C$?

A sinusoidal model is given by $y=3\sin(4x-1)+2$, where $x$ is measured in radians. What is the period of the model?

Which expression is equivalent to $\sin\theta$ by a cofunction identity?

True or false: The notation $\sin^{-1}x$ means $\frac{1}{\sin x}$.

For the equation $\tan x=1$, what is the exact reference angle in radians?

An oblique triangle has angles $A=42^\circ$ and $B=71^\circ$. What is angle $C$?

For values of $\theta$ where both sides are defined, which expression is equivalent to $\frac{1-\cos^2\theta}{\sin\theta}$?

Solve $2\sin x=\sqrt{3}$ on the interval $[0,2\pi)$.