Download Find reference angles: Sketch each angle. Then find its reference

12.2 DAY 1: FUNCTIONS OF ANY ANGLE
VOCABULARY
An angle is formed by two rays that have a common endpoint, called the vertex.
ANGLE
INITIAL SIDE
TERMINAL SIDE
STANDARD
POSITION
The fixed ray of an angle.
The ray that rotates about the vertex to get the
desired angle.
In a coordinate plane, an angle whose vertex is
at the origin and whose initial side is the positive
x-axis is in standard position.
The angle measure is POSITIVE if the rotation of an angle’s terminal side is
COUNTERCLOCKWISE.
The angle measure is NEGATIVE if the rotation of an angle’s terminal side is CLOCKWISE.
ANGLE MEASURE
POSITIVE VS.
NEGATIVE
REFERENCE ANGLE
Find reference angles: Sketch each angle. Then find its reference angle.
300
115
135
150
Angles are coterminal if their terminal sides coincide.
An angle coterminal with a given angle can be found by adding or subtracting multiples of ______.
Example:
COTERMINAL
Find one positive angle and one negative angle that are coterminal with a 95 degree angle.
95________________ = __________
95 ________________ = __________
12.2 DAY 2: FUNCTIONS OF ANY ANGLE
RADIANS AND DEGREES
Angles can be measured in degrees or radians just like distance can be measured in many different
ways. Radians are units that are based on arc length and circumference.
RADIANS
CONVERT BETWEEN
DEGREES AND
RADIANS
180   radians
Degrees to Radians
Radians to Degrees
To convert from degrees to radians, multiply the
number of degrees by
To convert from radians to degrees, multiply the
number of radians by
Degrees  radians

1
180
 radians 
180
 radians
Rewrite each degree measure in radians and each radian measure in degrees.
1. 330
5

2.
3. 
6
3
4.  50
5. 190
Remember the two special right triangle patterns:
6. 
7
3
12.2 FUNCTIONS OF ANY ANGLE
FINDING EXACT VALUES
SIGNS OF
TRIGONOMETRIC
FUNCTIONS
S
A
T
C
A
S
T
C
Draw the given angle and then determine whether the sine, cosine, and tangent functions of the given
angle are positive or negative.
1. 80
2. 115
Sin 80 
Cos 80 
Tan 80 
3. 325
Sin 115 
Cos 115 
Tan 115 
Sin 325 
Cos 325 
Tan 325 
4. 160
Sin  160 
Cos  160 
Tan  160 
12.1 Day 3: NOW WE HAVE TO PUT EVERYTHING TOGETHER!
Use a reference angle to find an Exact Trigonometric Value:
1.
2.
3.
4.
5.
Draw in the terminal side of the angle.
Determine the reference angle.
Draw in your special right triangle.
Use SOH CAH TOA to find the value.
Use A S T C to determine if the value is positive or negative.
sin 210
Reference Angle: ___________
SOH
CAH
Positive
or
TOA
Negative
sin 210  _________
5. cos 150
6. tan 315
Reference Angle: ___________
Positive
or
Negative
Reference Angle: ___________
cos  150  _______
Positive
or
Negative
tan 315  _______
8. cot  210
7. csc 225
Reference Angle: ___________
Reference Angle: ___________
Positive
9. cos
or
Negative
csc 225  _______
5
3
10. sec
Reference Angle: ___________
Positive
Positive
or
Negative
or
Negative
cot  210  _______
11
6
Reference Angle: ___________
cos
5
 _______
3
Positive
or
Negative
sec
11
 ________
6
12.2 DAY 4: FUNCTIONS OF ANY ANGLE
FINDING EXACT VALUES
Evaluate Trigonometric Functions Given a Point: Find the sin, cos, and tangent
1.
2.
QUADRANTAL
ANGLES
Evaluate the following.
3.
4.
Sin 270 = ______
Csc 270 = ______
Sin -90 = ______
Csc -90 = ______
Cos 270 = ______
Sec 270 = ______
Cos -90 = ______
Sec -90 = ______
Tan 270 = ______
Cot 270 = ______
Tan -90 = ______
Cot -90 = ______