Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
100
How do you convert from degrees to radians?
degrees*(π/180) = radians
100
Evaluate arcsin(1/2) on the unit circle:
π/6 & 5π/6
100
What is the formula to find the period of a function? What is the formula to find angular speed?
Period = 2π/b
v = r*w
100
A vector has a length of 15 and points in the direction of 210 degrees. Write the vector coordinates in component form.
w = <15cos(210), 15sin(210)>
100
Solve: sin(π/2)
1
200
What is the angle of 8 radians in degrees?
about 458 degrees
200
Solve for all solutions of tan(x) = 0.21
x = 0.207 + πk
200
A ferris wheel has a diameter of 50ft and is 5ft off the ground. It has an angular speed of 6 radians/minute. Write an equation to express a ferris wheel rider's height above the center of the wheel.
y = 25sin(6x)+5
200
Simplify the following: 2v + 4w
v = <7,8> and w = <3,5>
<26, 36>
200
Find all solutions to 2(tanx+3)=5+tanx (between 0 and 2π):
tanx = -1
x = 3π/4 and 7π/4
300
I have my dog on a leash tied in the middle of my yard. My dog walks as far as the leash will allow, which is 5 ft long. He then walks in a circle and then stops at an angle of 102 degrees. How far along the circle did my dog walk?
8.9 ft
300
A right triangle has side lengths of 4, 6, and 14. Find sine, cosine, and tangent ratios for the angle formed by the side lengths 6 and 14.
sin(x) = 4/14, cos(x) = 6/14, tan(x) = 4/6
300
What is the speed of a sine graph with period π/4?
8 rad/sec
300
Find the dot product of the following:
u = <3,5> and v = <6,1>
23
300
If the Side A is 8, Angle A is 56 degrees, Angle B is 78 degrees, what is the length of Side B?
B = 9.44
400
What is the magnitude of vector w = <12,5> ?
|w| = 13
400
A tree is 57 ft tall. Stanley is standing 15 ft away from the base of the tree. What is the angle of elevation from Stanley's feet to the top of the tree?
x = arctan(57/15) = 75.26 degrees
400
What is the amplitude, midline, period, vertical shift, and horizontal shift of the function y=sin(x+π/6)+1 ?
Amp: 1, midline: 1, period: 2π, vertical shift: +1, and horizontal shift: π/6 to the left
400
Simplify the following:
tan(x)sin(x)+sec(x)cos2(x)
sec(x)
400
An Angle is 75 degrees with one adjacent side being 10 and the other 9. What is the length of the third side?
x = 11.6
500
The point (x, 3/4) is on the unit circle. Find the value of x if a angle is formed from the 3 o'clock position.
x = +/- sqrt(7)/4
500
Suppose a 13-foot ladder is leaning against a building, reaching the bottom of a second-floor window 12 feet above the ground. What angle, in radians, does the ladder make with the building?
x = 22.62 degrees
500
What is the equation for the given graph?
y = -2sin(5x)
500
Simplify the following trig expression:
1 + sin2x
500
A quadrilateral has side lengths of 22, 26, 15, & 16. If the angle between sides 22 and 16 is 123°, what is the measure of the angle across from that angle?
106.5°