Trigonometric and Polar Functions — Quiz 1

Questions in this quiz (9)

1. Which of the following expressions is equivalent to $$\cos\theta$$?

   • $$\sin\left(\theta+\frac{\pi}{2}\right)$$
   • $$\sin\left(\theta-\frac{\pi}{2}\right)$$
   • $$\cos\left(\theta+\frac{\pi}{2}\right)$$
   • $$\cos\left(\frac{\pi}{2}-\theta\right)$$

2. At which value of $$x$$ does the graph of $$f(x)=\tan\left(x+\frac{\pi}{6}\right)$$ have a vertical asymptote?

   • $$\frac{\pi}{3}$$
   • $$\frac{\pi}{2}$$
   • $$\frac{\pi}{6}$$
   • $$\frac{2\pi}{3}$$

3. If $$f(x)=\cos(\sin^{-1}x)$$, what is the value of $$f\left(\frac{3}{5}\right)$$?

   • $$\frac{4}{5}$$
   • $$\frac{3}{5}$$
   • $$\frac{5}{4}$$
   • $$\frac{\sqrt{34}}{5}$$

4. If $$\sin x=\frac{5}{13}$$, $$\cos y=\frac{12}{13}$$, and $$x$$ and $$y$$ are acute angles, what is the value of $$\cos(x-y)$$?

   • $$\frac{119}{169}$$
   • $$1$$
   • $$\frac{144}{169}$$
   • $$\frac{25}{169}$$

5. Which of the following choices is equivalent to the expression $$\sin\theta(\csc\theta-\sin\theta)$$?

   • $$\cos^2\theta$$
   • $$\sin^2\theta$$
   • $$1-\sin^2\theta$$
   • $$1-\sin\theta$$

6. If the terminal side of angle $$A$$ in standard position is in Quadrant I and $$\sin A=\frac{12}{13}$$, what is the value of $$\cos A\cdot\tan A$$?

   • $$\frac{144}{169}$$
   • $$\frac{60}{169}$$
   • $$\frac{65}{144}$$
   • $$\frac{12}{13}$$

7. If $$x$$ is a positive acute angle and $$\sin x=a$$, which of the following is an expression for $$\tan x$$ in terms of $$a$$?

   • $$\frac{a}{\sqrt{1-a^2}}$$
   • $$\sqrt{1-a^2}$$
   • $$\frac{1-a}{a}$$
   • $$\sqrt{1-a^2}$$

8. If $$\tan x=1$$ and $$\cos x=-\frac{\sqrt{2}}{2}$$, find the measure of $$\angle x$$.

   • $$\frac{3\pi}{4}$$
   • $$\frac{\pi}{4}$$
   • $$\frac{5\pi}{4}$$
   • $$\frac{7\pi}{4}$$

9. The graph of which equation has an amplitude of $$1$$ and a period of $$\pi$$?

   • $$y=\sin x$$
   • $$y=2\sin 2x$$
   • $$y=\sin 2x$$
   • $$y=\frac{1}{2}\sin x$$