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6.1 Notes on Trigonometric Functions
Right-Triangle Trig:
SOHCAHTOA
sin( ) 
csc( ) 
cos( ) 
sec( ) 
tan( ) 
cot( ) 
Example 1: Find all ratios of the side lengths.
sin( ) 
csc( ) 
cos( ) 
sec( ) 
tan( ) 
cot( ) 
Example 2: Using trig to find missing side lengths.
Suppose you are 500 feet from the base of an office building, and suppose that the angle of
elevation of you line of sight (i.e., the angle between the horizontal ground and your diagonal line of
sight) to the top of the building is 36 degrees. How tall is the building?
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Reciprocal Functions:
sin( ) 
csc( ) 
cos( ) 
sec( ) 
tan( ) 
cot( ) 
Quotient Functions:
tan  
sin 
cos 
cot  
cos 
sin 
Special Right Triangles:
We can use this in trigonometry to find:
a.
cos(30) 
c.
cot(60 ) 
b. sin(45) 
d. csc(30 ) 
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Unit Circle:
Example 3: Solve the following.
1. cos

2. sin
3
4. tan
6. cos  = 
3
2
3
2
3. cos
5
4
5. sin
7. sin  =
5
6
11
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2
2
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Radians and Angles:
Draw an angle in standard position. Label the initial side, the terminal side, and the vertex.
There are two ways to measure angles: _____________________ and ___________________.
Degree measure: one degree is 1/360 of a circle
one full revolution is _______
one half revolution is _______
one quarter revolution is _______
Radian measure: one radian is a little less than 60° (draw the radian)
one full revolution is _______
one half revolution is _______
one quarter revolution is _______
Conversion equations:
radians X
180

= degrees
degrees X

= radians
180
Example 4: Change any degree measure to radians and any radian measure to degrees.
a. 360
b. π/4
c. π/3
d. 90°
e. 45°
f. π/6
g. 60°
h. 2π
i. 3π/4
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____________________________ are generated by counterclockwise rotation.
example: sketch 45°
sketch 2π/3
______________________________ are generated by clockwise rotation.
example: sketch –π/4
sketch -170°
__________________________ are angles that share an initial side and a terminal side.
Examples: Determine two coterminal angles (one positive and one negative) for each angle.
a. π/2
b. 35°
c. –π/3
d. 210°
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Extra Practice
1. Find the lengths of the sides of a 30-60-90 triangle whose shortest side is 5 units long.
2. Express 60 degrees in radians.
3. Express 3 radians in degrees.
4. Sketch the angle 
11
in standard position, and then use the unit circle to find the values of
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all six trigonometric functions of that angle.
5. Suppose you are 600 feet from the base of a building and the angle of elevation of your line of
sight to the top of the building is 30 degrees. How tall is the building?
Homework: IN THE BOOK pg. 414: #25, 27, 37-63odd
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