Trigonometry Exam

Convert (2, 3π/2) to Cartesian coordinates.

(0, -2)

Position vectors u and v have terminal points of (-6, 3) and (4, -2), respectively. Find the resulting terminal point of 2v - u.

(14, -7)

Simplify arcsin(-1/2).

-30°

θ is in standard position, and the terminal side passes through the point (3, -5). Find sinθ.

-5√34/34

sin(2π - x) =

-sinx

Determine the number of possible triangles, ABC, that can be formed given A = 30°, a = 7, and b = 18.

0

The range of F(x) = sin2x + 1 is _____.

0 ≤ F(x) ≤ 2

α and β are angles in standard position with terminal sides that lie in Quadrant I. If cosα = 4/5 and sinβ = 3/5, find cos(α - β).

1

Evaluate sin2(5π/4).

1/2

Convert 4π/5 to degrees.

144°

A triangular lot bounded by three streets has a length of 300 feet on one street, 200 feet on the second, and 120 feet on the third. The smallest angle formed by the streets is 30°. Find the area of the lot.

15,000 ft²

A point on the rim of a wheel moves with a velocity of 60 feet per second. Find the angular velocity of the point if the diameter of the wheel is 6 feet.

20 rad/sec

Given the following triangle, if c = √5 and a = 2, find the measure of ∠B to the nearest degree.

27

Which of the following angles is coterminal with -4π/3?

2π/3

Evaluate sec330°.

2√3/3

Determine the number of solutions to the equation 2cos²x + 3cosx + 1 = 0 for 0 ≤ x ≤ 2pi.

3

In which quadrant does θ terminate if cscθ < 0 and tanθ > 0?

III

As the angle between two vectors increases from 0° to 90°, their dot product _____.

decreases

Identify the conic whose equation is given. r = 1/3+2sinθ

ellipse

Choose the graph of y = 1/2cosx.

https://ibb.co/7g6gbmd

Convert x² + y² - y = 0 to a polar equation.

r = sinθ

Simplify cosθ + cosθtan²θ.

secθ

Which of the following is not equal to the other values?

sin143°

tan30-tan20/1+tan30tan20

tan10°

If angle θ is an acute angle such that cosθ = 1/4, find sinθ/2.

√6/4

If cos²x + 2cosx - 2 = 0, then cosx = _____.

-1 ± √3

Find z1 ÷ z2 for z1 = 9(cos⁡225∘+isin⁡225∘) and z2 = 3(cos⁡45∘+isin⁡45∘). Express the quotient in a+bi form.

-3

In triangle ABC, a = 12, B = 25°, and C = 45°. Find b.

5.4

The modulus of (3 + 4i)^4 is _____.

625

A pole is braced with a wire from the top of a pole to the ground. The wire is 100 feet long and makes an angle of 40° with the ground. Find the height of the pole.

64 ft

If θ is an angle in standard position that passes through (3, 4), find sin2θ.

24/25

Choose the graph of y = cotx.

https://ibb.co/HNDQBTR

Which of the following functions has a period of 4π?

y = sin1/2x

A sled is being pulled across a floor by two ropes such that the angle between them is 60°. If the forces on the ropes are 100 pounds and 80 pounds, what is the resultant of the forces?

156 lb

A river is flowing at the rate of 1.5 miles an hour when a boy rows across it. Find the resulting speed of the boat if the boy rows at a still-water speed of 2.6 miles per hour and heads the boat perpendicular to the direction of the current.

3 mph

What is the vertical component of a 100 pound force applied at 30° above the horizontal?

50 pounds

The sides of an isosceles triangle are 3, 3, and 4. Find the measure of the vertex angle to the nearest degree.

84°

Choose the graph of the polar equation r = cos2θ.

https://ibb.co/RjTGK1k

If 90° < θ < 180° and cotθ = -1/3, then cscθ = _____.

√10/3

Choose the polar form of the complex number -1 + i.

√2(cos135° + isin135°