Q: Which of the following is the correct definition of the sine function for an angle $$\theta in a $$right triangle?

$$\sin \theta = \dfrac{\text{opposite}}{\text{hypotenuse}}$$

Q: Which identity is known as the Pythagorean Identity?

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

Q: Which of the following is the correct double-angle identity for $$\sin 2\theta$$?

$$\sin 2\theta = 2\sin \theta \cos \theta$$

Q: Which of the following is the correct expression for $$\tan(\alpha - \beta)$$?

$$\dfrac{\tan \alpha - \tan \beta}{1 + \tan \alpha \tan \beta}$$

Q: Which of the following is the correct half-angle identity for $$\sin^2$ \theta$$?

$$\sin^2$ \theta = \dfrac{1 - \cos 2\theta}{2}$$

Q: A triangle has sides $$a = 7$$, $$b = 9$$, and angle $$C = 60^\circ. $$What is the area of the triangle?

$$\dfrac{1}{2} \times 7 \times 9 \times \sin 60^\circ$$

Question 1

Which of the following is the correct definition of the sine function for an angle $$	heta in a $$right triangle?

Accepted Answer

$$\sin 	heta = \dfrac{	ext{opposite}}{	ext{hypotenuse}}$$

Question 2

A ladder leans against a wall making a $$60^\circ$$ angle with the ground. If the foot of the ladder is $$4$$ meters from the wall, how long is the ladder?

Accepted Answer

$$4 \div \cos 60^\circ$$

Question 3

Which of the following is the correct value of $$\cos \left(\dfrac{3\pi}{2}\right)$$?

Accepted Answer

$$0$$

Question 4

If $$	an 	heta = 3$$ and $$	heta is in $$the second quadrant, what is $$\sin 	heta$$?

Accepted Answer

$$-\dfrac{3}{\sqrt{10}}$$

Question 5

Which identity is known as the Pythagorean Identity?

Accepted Answer

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

Question 6

A Ferris wheel with a radius of $$10$$ meters makes one complete revolution every $$30$$ seconds. What is the angular speed of the wheel in radians per second?

Accepted Answer

$$\dfrac{\pi}{15}$$

Question 7

Given $$\sin \alpha = \dfrac{5}{13}$$ and $$\alpha is in $$Quadrant II, what is $$\cos \alpha$$?

Accepted Answer

$$-\dfrac{12}{13}$$

Question 8

Which of the following is the correct formula for the Law of Sines?

Accepted Answer

$$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$$

Question 9

Solve for $$x in$$ $$2\sin x - 1 = 0$$ for $$0 \leq x \u003c 2\pi.$$

Accepted Answer

$$x = \dfrac{\pi}{6}, \dfrac{5\pi}{6}$$

Question 10

Which of the following is the correct double-angle identity for $$\sin 2	heta$$?

Accepted Answer

$$\sin 2	heta = 2\sin 	heta \cos 	heta$$

Question 11

A ship sails $$8 km $$east and then $$6 km $$north. What is the straight-line distance from the starting point to the final position?

Accepted Answer

$$10 km$$

Question 12

If $$\cos 	heta = -\dfrac{3}{5}$$ and $$	heta is in $$the third quadrant, what is $$\sin 	heta$$?

Accepted Answer

$$-\dfrac{4}{5}$$

Question 13

Which of the following is the correct sum identity for $$\cos(A+B)$$?

Accepted Answer

$$\cos(A+B) = \cos A \cos B - \sin A \sin B$$

Question 14

A vector has magnitude $$5$$ and direction $$53^\circ$$ north of east. What are its rectangular components?

Accepted Answer

$$5\cos 53^\circ$$ east, $$5\sin 53^\circ$$ north

Question 15

Which of the following is the correct expression for $$	an(\alpha - \beta)$$?

Accepted Answer

$$\dfrac{	an \alpha - 	an \beta}{1 + 	an \alpha 	an \beta}$$

Question 16

If $$\sin 	heta = 0.6$$ and $$	heta is in $$the first quadrant, what is $$	heta in $$degrees (rounded to the nearest degree)?

Accepted Answer

$$37^\circ$$

Question 17

Which of the following is the correct half-angle identity for $$\sin^2$ 	heta$$?

Accepted Answer

$$\sin^2$ 	heta = \dfrac{1 - \cos 2	heta}{2}$$

Question 18

A triangle has sides $$a = 7$$, $$b = 9$$, and angle $$C = 60^\circ. $$What is the area of the triangle?

Accepted Answer

$$\dfrac{1}{2} 	imes 7 	imes 9 	imes \sin 60^\circ$$

Question 19

Which of the following is the correct formula for converting degrees to radians?

Accepted Answer

$$	ext{radians} = 	ext{degrees} 	imes \dfrac{\pi}{180}$$

Plane Trigonometry Syllabus and Course Structure – MATH 1316

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