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(cos225∘+isin225∘) and z2 = 3(cos45∘+isin45∘). 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°