Name:______________________________
Class: __________________ Per: _____
TRIG REVIEW
List of topics:
Intro to Trigonometry
How to Convert Between Radians and Degrees
How to Find Reference and Equivalence Angles
How to Use Special Triangles to Find Coordinates Along a Unit Circle
How to Find Coordinates Along a Non-Unit Circle
REVIEW: SOH-CAH-TOA
How to Evaluate Sine
How to Transform Sine Graphs
How to Evaluate Cosine
How to Transform Cosine Graphs
How to Evaluate Tangent
How to Evaluate Reciprocal Trig Functions
How to Evaluate Inverse Trig Functions (Arcs)
How to Create Proofs Using the Pythagorean Identities
How to Use the Angle Sum Identities
How to Use the Half Angle and Double Angle Identities
Some good vocab terms to know:
Trigonometry
Equivalence angle
Reference triangles
Origin
Clockwise
Tangent
Legs
Frequency
Vertical shift
Rotation
Arc function
Reciprocal
Cotangent
Arcotangent
Double Angle
Identities
Angle
Reference angle
30-60-90
Radius
Counterclockwise
Opposite
Coordinates
Cycle
Phase shift
Pythagorean
theorem
Arcsin
Reciprocal trig
function
Inverse reciprocal
trig function
Trig identities
Solve
Radians
Unit circle
45-45-90
Diameter
Sine
Adjacent
Transformation
Period
Speed
Trig function
Degrees
Conversion
Cardinal points
Orientation
Cosine
Hypotenuse
Amplitude
Horizontal shift
Length
Inverse trig function
Arcos
Secant
Arctan
Cosecant
Arcsecant
Arcosecant
Trig Angle Sum
Identities
Prove
Trig Angle Difference
Identities
Verify
I. Convert the following angles from degrees to radians or radians to degrees.
Then plot them on the unit circle, state which quadrant they fall in, and
determine the equivalence and reference angles of each.
-165°
9𝜋
13
2°
29𝜋
645°
11𝜋
9
-165°
9𝜋
13
2°
29𝜋
645°
11𝜋
9
-
-
13
13
II. Find the coordinates of the following angles.
90°
3
𝜋
2
120°
2
− 𝜋
3
-180°
-330°
135°
5
− 𝜋
6
13
𝜋
6
𝜋 on a circle with cardinal
coordinates of (2,1), (-2,-3)
(2,-7) and (6,-3).
390° on a unit circle that has
been shifted four units right
and six units down.
7𝜋 on a circle with a
diameter of 4 centered at
(0,-2)
13
4
135° on a circle with a
radius of 0.5 centered at
(-2,3).
2
− 3 𝜋 on a circle that has a
radius of 5.
330° on a circle with
diameter of 6 .
III. Calculate the sin, cos, tan, sec, csc, and cot of the following angles:
-120°
4
𝜋
3
-210°
15
𝜋
4
495°
13
𝜋
3
-225°
-405°
−
11
𝜋
6
V. Graph the following:
2
y = -sin(Θ + 3 𝜋) + 5
2
y = -2cos(Θ + 5 𝜋) - 4
y = 3sin(2Θ) - 2
1
𝜋
y = 5cos(4Θ - 3 )
1
1
1
1
y = -4sin(2Θ + 4 𝜋) - 1
y = -15cos(2Θ + 4 𝜋) -10
VI. Write a positive sin, negative sin, positive cos, and negative cos equation
for each of the graphs. ALSO write the domain and range of the following:
V. Calculate the following. WRITE ALL ANGLE MEASURES IN RADIANS.
𝑥
cos(tan-1(3))
tan-1(sin(-1))
csc-1(tan(sin-1(2)))
tan-1(sec(𝜋))
sin(cos-1(3x))
sin(cot-1(-1))
cos-1(sin(−
sin(cos-1−
2
√2
))
2
2𝜋
3
))
sec-1(csc(4π))
VI. Solve for the following. WRITE ALL THE ANGLE MEASURES IN RADIANS.
Calculate the exact values for each.
#9:
#10
#11
#12
#13
#14
#15
#16
VII. Prove the following:
VIII. Use the sum/difference formulas to rewrite the following and then
calculate:
cos(105°)
sec(-145°)
6𝜋
tan( )
12
21𝜋
sin(
12
)