Q: Which of the following is a Pythagorean identity?

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

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

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

Question 1

Which of the following best describes a coterminal angle to $$1106^{\circ}$$ with the least positive measure?

Accepted Answer

$$26^{\circ}$$

Question 2

A wheel rotates at $$270$$ revolutions per minute. Through how many degrees does a point on the edge of the wheel move in $$5$$ seconds?

Accepted Answer

$$81000^{\circ}$$

Question 3

Given that $$	riangle ABC is $$similar to $$	riangle DEF$$, which of the following must be true?

Accepted Answer

Corresponding angles are congruent and corresponding sides are proportional.

Question 4

If the measure of one angle in a triangle is $$33^{\circ}$$ and another is $$26^{\circ}$$, what is the measure of the third angle?

Accepted Answer

$$121^{\circ}$$

Question 5

Joey, who is $$63$$ inches tall, casts a $$42$$ inch shadow at the same time a tree casts a $$38$$ foot shadow. What is the height of the tree in feet?

Accepted Answer

$$57 ft$$

Question 6

Convert $$105^{\circ} 20$$' 32''$$ to decimal degrees to the nearest thousandth.

Accepted Answer

$$105.342^{\circ}$$

Question 7

Which of the following is NOT a possible value for $$\cos 	heta$$?

Accepted Answer

$$-1.7$$

Question 8

Given $$	an 	heta \u003e 0$$ and $$\csc 	heta \u003c 0$$, in which quadrant(s) could $$	heta be $$located?

Accepted Answer

Quadrant III

Question 9

If $$\sin 	heta = -\dfrac{5}{\sqrt{89}}$$ and $$	heta is in $$Quadrant III, what is $$\cos 	heta$$?

Accepted Answer

$$-\dfrac{8}{\sqrt{89}}$$

Question 10

Which trigonometric functions are always undefined for angles whose terminal side lies on the $$y-$$axis?

Accepted Answer

Cotangent and cosecant

Question 11

Given $$\cot 	heta = -2$$ and $$	heta is in $$Quadrant II, what is $$\sin 	heta$$?

Accepted Answer

$$\dfrac{24}{25}$$

Question 12

Which of the following is a Pythagorean identity?

Accepted Answer

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

Question 13

If $$\cos 	heta = \dfrac{2}{\sqrt{20}}$$, what is $$\sec 	heta$$?

Accepted Answer

$$\sqrt{5}$$

Question 14

A right triangle has legs of length $$8$$ and $$15. $$What is the length of the hypotenuse?

Accepted Answer

$$17$$

Question 15

Which of the following is the correct reciprocal identity for $$\csc 	heta$$?

Accepted Answer

$$\csc 	heta = \dfrac{1}{\sin 	heta}$$

Question 16

If the terminal side of an angle in standard position passes through the point $$(8, -6)$$, what is $$\sin 	heta$$?

Accepted Answer

$$-\dfrac{3}{5}$$

Question 17

Which of the following statements about the range of the tangent function is correct?

Accepted Answer

The range is $$(-\infty, \infty)$$

Question 18

If $$\sin 	heta = 0.6$$ and $$	heta is in $$Quadrant II, what is $$\cos 	heta$$?

Accepted Answer

$$-0.8$$

Question 19

Which of the following best describes a quadrantal angle?

Accepted Answer

An angle whose terminal side lies on the $$x-$$axis or $$y-$$axis

Question 20

If $$	an 	heta = 3$$ and $$	heta is in $$Quadrant III, what is the sign of $$\sin 	heta$$ and $$\cos 	heta$$?

Accepted Answer

Both are negative

Angles, Angle Relationships, and Trigonometric Functions: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards