Unit Circle (Degrees/radians)
Quadrants
Unit Circle
Evaluate Trig Functions Given a Point
Word Problems
100
sin 4π/3
-√3/2
100
What quadrant is sin, cos and tan positive
I
100
What is the radius in the unit circle?
1
100
Find r (the radius) given point on the terminal side of an angle of rotation θ 
r=10
100
Two scuba divers are diving at different depths along the same line of sight to the boat as shown. Which trigonometric function would you use to find the distance each diver is from the boat along the line of sight?
Sine
The hypotenuse is needed. Sine is the trigonometric function that relates the opposite side to the hypotenuse.
200
cos 270
0
200
What quadrant is cosine positive and sine is negative?
IV
200
The number of radians in a complete rotation is approximately
2pi
200
Given a point on the terminal side of an angle of rotation θ, find tanθ
tan(theta)=-8/6 =-4/3
200
Find the distance of diver A from the boat
sin(-54)=120/h
h=120/sin(-54)
h=-148.33
148.33 ft
300
tan 210
sqrt3/3
300
What quadrants is tangent positive?
Quadrants I and III
300
What are 2 possible measures for theta in degrees if
sin theta=-sqrt3/2
240 degrees and 300 degrees
300
Use the given point on the terminal side of an angle of rotation θ to evaluate sinθ
sin(theta)=4/5
300
Find the distance of diver B from the boat
sin(-54)=150/h
h=150/sin(-54)
h=-185.41
185.41 ft
400
tan(90)
undefined
400
If cos is negative and sin is positive than tan is
NEGTATIVE
400
The measure of theta in radians if the coordinates are
(sqrt3/2, -1/2)
(11pi)/6
400
Use the given point on the terminal side of an angle of rotation θ to evaluate cos θ
cos(theta)=3/5
400
How much farther from the boat along the line of sight is Diver B than Diver A?
185.41-148.33=37.08 ft
500
tan 11π/6
-sqrt3/3
500
When is Tan θ=undefined
when x=0, (0,1) and (0,-1)
500
What are 2 possible measures for theta in degrees if
tan(theta)=-1
135 and 315
500
if sin(x)=4/5 and x lies in the 2nd quadrant, find cos(x)
-3/5
500
Caroline is riding the Ferris wheel at the carnival. The wheel has a diameter of 250 feet. When she gets into the car for her ride, she is 5 feet above the ground. After 2 minutes the Ferris wheel stops and her car forms a 60°-angle with the center of the wheel. How far from the ground is Caroline at this time?
sin(60)=x/125
125sin(60)=x
x=108.25
125+5+108.25=236.25ft