FiltersDone

Question type

Essay

Multiple Choice

Short Answer

True False

Matching

Exam 9: Trigonometric Identities and Equations

Show Answer

Share

---

All types

Filters

Study Flashcards

Question 51

Short Answer

Review LaterAdd Note

Review Later

Solve each equation or inequality over the indicated interval. - $\sin 2 \theta+3 \cos \theta=0, \quad\left[0^{\circ}, 360^{\circ}\right)$

Correct Answer

verified

Show Answer

Question 52

Short Answer

Review LaterAdd Note

Review Later

Solve each equation or inequality over the indicated interval. - $2 \sin x+\sqrt{3} \leq 0, \quad[0,2 \pi)$

Correct Answer

verified

Show Answer

Question 53

Essay

Review LaterAdd Note

Verify that each equation is an identity. - $\csc ^{2} x+\cot ^{2} x=\frac{1+\cos ^{2} x}{1-\cos ^{2} x}$

Solve each equation or inequality over the indicated interval. - $2 \cos x-1 \leq 0, \quad[-\pi, \pi]$

Find the exact value of each expression. - $\cos ^{-1}\left(\cos \frac{3 \pi}{2}\right)$

Consider the function defined by $f(x)=3 \cos ^{-1} x$ . (a) Sketch the graph. (b) Give the domain and range. (c) Explain why $f(1.2)$ is not defined.

Solve each equation or inequality over the indicated interval. - $\cos ^{2} \theta-2 \cos \theta-3=0, \quad\left[0^{\circ}, 360^{\circ}\right)$

Given $\sin y=\frac{3}{5}, \cos x=-\frac{1}{4}$ with $\frac{\pi}{2}<x<\pi$ and $\frac{\pi}{2}<\mathrm{y}<\pi$ , find the exact values for the following: - $\cos (x+y)$

Use an identity to write each expression as a trigonometric function of $\theta$ alone. - $\sin \left(\theta+90^{\circ}\right)$

Verify that each equation is an identity. - $(\sin x+\cos x)^{2}=\sin 2 x+1$

Consider the function defined by $f(x)=-\frac{1}{3} \sin ^{-1} x$ . (a) Sketch the graph. (b) Give the domain and range. (c) Explain why $f(-2)$ is not defined.

Suppose that the formula $A(t)=-\frac{1}{2} \cos \frac{\pi}{8} t+\frac{1}{6}$ describes the motion formed by a rhythmically moving arm during a 16 minute time period where $A(t)$ is the angle (in radians) formed by the arm at time $t$ (in minutes). (a) Give the domain and range of $A$ . (b) Graph $A(t)$ over its domain. (c) Use the graph to determine the maximum and minimum values of $A(t)$ and when they occur. (d) Find $A(6)$ analytically and check your result graphically. Use symmetry to find $A(10)$ . (e) When is the angle $\frac{1}{6}$ radians? (f) Write the equation $A=-\frac{1}{2} \cos \frac{\pi}{8} t+\frac{1}{6}$ as an equation involving arcsine by solving for $t$ .

Given $\sin y=-\frac{4}{5}, \cos x=\frac{1}{2}$ with $\frac{3 \pi}{2}<x<2 \pi$ and $\pi<y<\frac{3 \pi}{2}$ , find the exact values for the following: - $\sin 2 x$

Consider the function defined by $f(x)=4 \sin ^{-1} 2 x$ . (a) Sketch the graph. (b) Give the domain and range. (c) Explain why $f(.9)$ is not defined.

Write as an algebraic expression in $u, u>0$ . - $\cos \left(\tan ^{-1} u\right)$

Find the exact value of each expression. - $\arctan (\sqrt{3})$

Verify that each equation is an identity. - $\frac{\sin ^{2} 2 x}{1+\cos 2 x}=2 \sin ^{2} x$

Find the exact value of each expression. - $\sec ^{-1}\left(-\frac{2 \sqrt{3}}{3}\right)$

Solve each equation or inequality over the indicated interval. - $\sec \frac{x}{4}=\cos \frac{x}{4}, \quad[0,4 \pi)$

Solve each equation or inequality over the indicated interval. - $\cot \frac{x}{4}=\tan \frac{x}{4}, \quad[0,4 \pi)$