$$\sin(\cot \theta + \tan \theta) = \sec \theta$$

Question 1

Which of the following is a correct identity for $$\sin(\cot 	heta + 	an 	heta)$$?

Accepted Answer

$$\sin(\cot 	heta + 	an 	heta) = \sec 	heta$$

Question 2

Given $$\sec x = \frac{3}{2}$$ and $$\csc y = 3$$, with $$x$$ and $$y in $$Quadrant I, what is $$	an(x+y)$$?

Accepted Answer

$$\frac{1}{2}(2 + \sqrt{5})$$

Question 3

If $$\sin x = \frac{5}{13}$$ and $$x is in $$Quadrant I, what is $$\cos x$$?

Accepted Answer

$$\frac{12}{13}$$

Question 4

Solve for $$x in $$the interval $$[0, 2\pi)$$: $$4\sin x = 3$$

Accepted Answer

$$x = \arcsin\left(\frac{3}{4}\right)$$ and $$x = \pi - \arcsin\left(\frac{3}{4}\right)$$

Question 5

Which of the following is equivalent to $$\cos^2$ x - \sin^2$ x$$?

Accepted Answer

$$\cos 2x$$

Question 6

Given $$\vec{u} = \langle 2, 7 \rangle$$ and $$\vec{v} = \langle 5, 9 \rangle$$, what is $$\vec{u} + \vec{v}$$?

Accepted Answer

$$\langle 7, 16 \rangle$$

Question 7

If $$	an x = \frac{5}{12}$$ and $$x is in $$Quadrant II, what is $$\sin x$$?

Accepted Answer

$$-\frac{5}{13}$$

Question 8

Find the magnitude and direction (in degrees) of the vector $$\vec{v} = \langle 1, 2 \rangle.$$

Accepted Answer

Magnitude: $$\sqrt{5}$$, Direction: $$63.43^\circ$$

Question 9

Which of the following is a correct simplification for $$\frac{\sin x}{\cos x}$$?

Accepted Answer

$$	an x$$

Question 10

If $$\cos x = 0.65$$, what is $$x in $$radians (rounded to two decimal places)?

Accepted Answer

$$x \approx 0.86$$

Question 11

Which of the following is a correct identity for $$\cos(x + \frac{\pi}{4}) + \sin(x - \frac{\pi}{4})$$?

Accepted Answer

$$\cos(x + \frac{\pi}{4}) + \sin(x - \frac{\pi}{4}) = 0$$

Question 12

Given $$\cos x = \frac{5}{13}$$ and $$x is in $$Quadrant I, what is $$\sin x$$?

Accepted Answer

$$\frac{12}{13}$$

Question 13

Which of the following is the correct value for $$\sin 15^\circ$$?

Accepted Answer

$$\frac{\sqrt{6} - \sqrt{2}}{4}$$

Question 14

If $$\vec{u} = \langle -1, 5 \rangle$$ and $$\vec{v} = \langle 10, -4 \rangle$$, what is $$\vec{u} - \vec{v}$$?

Accepted Answer

$$\langle -11, 9 \rangle$$

Question 15

Which of the following is a correct simplification for $$\frac{1}{\sin x}$$?

Accepted Answer

$$\csc x$$

Question 16

Solve for $$x in$$ $$\sin^2$ x - \cos x = 0 in$$ $$[0, 2\pi).$$

Accepted Answer

$$x = \frac{\pi}{2}, \frac{5\pi}{6}, \frac{7\pi}{6}$$

Question 17

Which of the following is a correct value for $$	an 75^\circ$$?

Accepted Answer

$$2 + \sqrt{3}$$

Question 18

If $$\vec{u} = \langle 3, 4 \rangle$$, what is the magnitude of $$\vec{u}$$?

Accepted Answer

$$5$$

Question 19

Which of the following is a correct value for $$\cos 75^\circ$$?

Accepted Answer

$$\frac{\sqrt{6} + \sqrt{2}}{4}$$

Comprehensive Trigonometry Study Guide: Identities, Equations, and Vectors

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