Q: Which of the following is a correct reciprocal identity?

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

Q: Given $$\tan \theta = \dfrac{2}{3}$$ for an acute angle $$\theta$$, what is $$\sin \theta$$?

$$\sin \theta = \dfrac{2}{\sqrt{13}}$$

Q: Which of the following is a Pythagorean identity?

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

Q: A ladder leans against a wall forming an angle $$\theta$$ with the ground. If the ladder is 13 ft long and the base is 5 ft from the wall, what is $$\sin \theta$$?

$$\sin \theta = \dfrac{12}{13}$$

Q: Which identity expresses $$\tan \theta in $$terms of $$\sin \theta$$ and $$\cos \theta$$?

$$\tan \theta = \dfrac{\sin \theta}{\cos \theta}$$

Q: If $$\sin \theta = \dfrac{1}{3}$$ and $$\theta is $$acute, what is $$\cos \theta$$?

$$\cos \theta = \dfrac{\sqrt{8}}{3}$$

Q: Which of the following is a correct statement of the Complementary Angle Theorem?

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

Q: Given $$\tan \theta = \dfrac{2}{3}$$ and $$\theta is $$acute, what is $$\sec \theta$$?

$$\sec \theta = \dfrac{\sqrt{13}}{3}$$

Q: A ramp rises 2 meters over a horizontal distance of 3 meters. What is $$\sin \theta$$ for the angle $$\theta$$ the ramp makes with the ground?

$$\sin \theta = \dfrac{2}{\sqrt{13}}$$

Q: If $$\sin \theta = \dfrac{1}{2}$$ and $$\theta is $$acute, what is $$\tan \theta$$?

$$\tan \theta = \dfrac{1}{\sqrt{3}}$$

Question 1

Given a right triangle with sides $$a = 5$$, $$b ($$opposite), and hypotenuse $$c = 13$$, what is the value of $$b$$?

Accepted Answer

$$b = 12$$

Question 2

If $$\sin 	heta = \dfrac{3}{5}$$ and $$	heta is an $$acute angle, what is $$\cos 	heta$$?

Accepted Answer

$$\cos 	heta = \dfrac{4}{5}$$

Question 3

Which of the following is a correct reciprocal identity?

Accepted Answer

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

Question 4

Given $$	an 	heta = \dfrac{2}{3}$$ for an acute angle $$	heta$$, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = \dfrac{2}{\sqrt{13}}$$

Question 5

If $$\sin 	heta = \dfrac{1}{2}$$ and $$	heta is $$acute, what is $$\sec 	heta$$?

Accepted Answer

Question 6

Which of the following is a Pythagorean identity?

Accepted Answer

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

Question 7

If $$\sin 	heta = \dfrac{1}{2}$$ and $$	heta is $$acute, what is $$\cot 	heta$$?

Accepted Answer

$$\cot 	heta = \sqrt{3}$$

Question 8

A ladder leans against a wall forming an angle $$	heta$$ with the ground. If the ladder is 13 ft long and the base is 5 ft from the wall, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = \dfrac{12}{13}$$

Question 9

If $$	an 	heta = \dfrac{b}{a}$$, which of the following is true for $$\cot 	heta$$?

Accepted Answer

$$\cot 	heta = \dfrac{a}{b}$$

Question 10

Which identity expresses $$	an 	heta in $$terms of $$\sin 	heta$$ and $$\cos 	heta$$?

Accepted Answer

$$	an 	heta = \dfrac{\sin 	heta}{\cos 	heta}$$

Question 11

If $$\sin 	heta = \dfrac{1}{3}$$ and $$	heta is $$acute, what is $$\cos 	heta$$?

Accepted Answer

$$\cos 	heta = \dfrac{\sqrt{8}}{3}$$

Question 12

Which of the following is a correct statement of the Complementary Angle Theorem?

Accepted Answer

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

Question 13

Given $$	an 	heta = \dfrac{2}{3}$$ and $$	heta is $$acute, what is $$\sec 	heta$$?

Accepted Answer

$$\sec 	heta = \dfrac{\sqrt{13}}{3}$$

Question 14

If $$\sin 	heta = \dfrac{1}{2}$$, what is $$\csc 	heta$$?

Accepted Answer

$$\csc 	heta = 2$$

Question 15

A ramp rises 2 meters over a horizontal distance of 3 meters. What is $$\sin 	heta$$ for the angle $$	heta$$ the ramp makes with the ground?

Accepted Answer

$$\sin 	heta = \dfrac{2}{\sqrt{13}}$$

Question 16

If $$\sin 	heta = \dfrac{1}{2}$$ and $$	heta is $$acute, what is $$	an 	heta$$?

Accepted Answer

$$	an 	heta = \dfrac{1}{\sqrt{3}}$$

Question 17

Which of the following is a quotient identity?

Accepted Answer

$$	an 	heta = \dfrac{\sin 	heta}{\cos 	heta}$$

Question 18

If $$\sin 	heta = \dfrac{1}{2}$$ and $$	heta is $$acute, what is $$\cos(90^\circ - 	heta)$$?

Accepted Answer

$$\cos(90^\circ - 	heta) = \dfrac{1}{2}$$

Question 19

If $$	an 	heta = \dfrac{2}{3}$$ and $$	heta is $$acute, what is $$\cot 	heta$$?

Accepted Answer

$$\cot 	heta = \dfrac{3}{2}$$

Right Triangle Trigonometry: Trigonometric Functions and Fundamental Identities

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