Download 4-1: RIGHT TRIANGLE TRIGONOMETRY  RIGHT TRIANGLE TRIGONOMETRIC FUNCTIONS

4-1: RIGHT TRIANGLE
TRIGONOMETRY
Precalculus
Mr. Gallo
RIGHT TRIANGLE TRIGONOMETRIC FUNCTIONS
Six Trigonometric Functions
sine    sin  
opp
hyp
cosine    cos  
adj
hyp
tangent    tan  
opp
adj
cosecant    csc  
secant    sec  
hyp
opp
Hypotenuse
Opposite
hyp
adj
cotangent    cot  
adj
opp

Adjacent
 Reciprocal Trigonometric Functions
 Cosecant, secant and cotangent
 Ratios are reciprocals of sine, cosine and tangent respectively
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RIGHT TRIANGLE TRIGONOMETRIC FUNCTIONS
Inverse Trigonometric Functions
 Used to find the measure of an acute angle
Hypotenuse
Opposite
If sin   x, then sin x  
1
If cos   x, then cos 1 x  

If tan   x, then tan 1 x  
Adjacent
ANGLES OF ELEVATION AND DEPRESSION
Angle of Elevation
 The angle above horizontal that an observer must look to see an object that is
higher than the observer. It is congruent to the angle of depression.
Angle of Depression
 The angle below horizontal that an observer must look to see an object that is
lower than the observer. It is congruent to the angle of elevation.
Angle of Depression
Angle of Elevation
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SPECIAL RIGHT TRIANGLES
45°
45°
90°

sin 
45
x
2
x
cos 
45
tan 
x
30°
60°
90°
csc 
60
2x
x
30
x 3
30
45
60
1
2
3
2
3
2
3
3
2
sec  2 3 3
cot 
3
2
2
2
1
2
2
1
3
2
2 3
2
2
1
3
3
3
Homework: p.227 #1, 5, 11, 15, 21, 23, 27, 30, 31, 35, 39, 40, 45, 74
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