Q: Which of the following is the reciprocal identity for $$\\sin \\theta$$?

$$\\sin \\theta = \\frac{1}{\\csc \\theta}$$

Q: Which of the following is the correct Pythagorean identity?

$$\\sin^2$ \\theta + \\cos^2$ \\theta = 1$$

Q: Which of the following is the cofunction identity for sine?

$$\\sin \\theta = \\cos(90^\\circ - \\theta)$$

Q: Which of the following is the correct reciprocal identity for $$\\tan \\theta$$?

$$\\tan \\theta = \\frac{1}{\\cot \\theta}$$

Question 1

Which of the following best describes a positive angle in standard position?

Accepted Answer

An angle whose initial side is on the positive x-axis and is measured counterclockwise from the initial side.

Question 2

If an angle measures $$50^\circ$$, which of the following is a positive coterminal angle?

Accepted Answer

$$410^\circ$$

Question 3

A right triangle has an opposite side of length 8 and an adjacent side of length 15. What is the length of the hypotenuse?

Accepted Answer

$$17$$

Question 4

Which of the following is the correct definition of the radian measure?

Accepted Answer

The measure of the central angle of a circle subtended by an arc equal in length to the radius of the circle.

Question 5

Convert $$120^\circ to $$radians.

Accepted Answer

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

Question 6

A circular arc has a radius of $$5$$ units and subtends a central angle of $$2$$ radians. What is the length of the arc?

Accepted Answer

$$10$$ units

Question 7

Which of the following is the reciprocal identity for $$\sin \theta$$?

Accepted Answer

$$\sin \theta = \frac{1}{\csc \theta}$$

Question 8

Given $$\sin \theta = \frac{3}{5}$$ and $$\theta is in $$the first quadrant, what is $$\cos \theta$$?

Accepted Answer

$$\frac{4}{5}$$

Question 9

Which of the following angles is complementary to $$35^\circ$$?

Accepted Answer

$$55^\circ$$

Question 10

A student is standing 400 meters from the base of Mt. Fuji, which is 12,400 ft high. What is the angle of elevation from the student to the peak, in degrees? (1 meter = 3.281 ft)

Accepted Answer

$$86.2^\circ$$

Question 11

Which of the following is the correct Pythagorean identity?

Accepted Answer

$$\sin^2$ \theta + \cos^2$ \theta = 1$$

Question 12

If $$\theta is an $$acute angle in a right triangle, which trigonometric function is defined as $$\frac{\text{adjacent}}{\text{hypotenuse}}$$?

Accepted Answer

$$\cos \theta$$

Question 13

Which of the following is the correct relationship between degrees and radians?

Accepted Answer

$$180^\circ = \pi$$ radians

Question 14

Which of the following is the cofunction identity for sine?

Accepted Answer

$$\sin \theta = \cos(90^\circ - \theta)$$

Question 15

If $$\tan \theta = \frac{5}{12}$$, what is $$\sec \theta$$?

Accepted Answer

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

Question 16

Which of the following is the correct reciprocal identity for $$\tan \theta$$?

Accepted Answer

$$\tan \theta = \frac{1}{\cot \theta}$$

Question 17

A right triangle has an angle $$\theta = 60^\circ$$, opposite side $$= 3$$, adjacent side $$= x. $$What is the value of $$x$$?

Accepted Answer

$$3\sqrt{3}/2$$

Question 18

Which of the following is the correct formula for the length of a circular arc?

Accepted Answer

$$s = r\theta$$

Question 19

If $$\sin \theta = \frac{5}{13}$$ and $$\theta is in $$the first quadrant, what is $$\tan \theta$$?

Accepted Answer

$$\frac{5}{12}$$

Angles, Their Measure, and Right Triangle Trigonometry

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