5.2.1 trigonometric functions
TRANSCRIPT
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5.2 Trigonometric Functions
Sine, Cosine, Tangent, Cosecant, Secant, Cotangent
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ry
x
siny
r
Sine
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ry
x
cosx
r
Cosine
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ry
x
tany
x
Tangent
sintan
cos
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ry
x
cscr
y
Cosecant
1csc
sin
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ry
x
secr
x
Secant
1sec
cos
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ry
x
cotx
y
Cotangent
coscot
sin
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Review - Special Right Triangles
21
1
45 30
3
2 1
60
32
1
454
603
306
You MUST know these!
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Find the exact value of the trig functions for the given angle
315 Quadrant IV
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Find the exact value of the trig functions for the given angle
315
Reference Angle 45⁰
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Find the exact value of the trig functions for the given angle
315
45
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Find the exact value of the trig functions for the given angle
315
45
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Find the exact value of the trig functions for the given angle
315
45
2-1
1
1sin 315
2
1 2sin 315
2 2
2sin315
2
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Find the exact value of the trig functions for the given angle
315
45
2-1
1
1cos315
2
1 2cos315
2 2
2cos315
2
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Find the exact value of the trig functions for the given angle
315
45
2-1
1
1tan315
1
tan315 1
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Find the exact value of the trig functions for the given angle
315
45
2-1
12
csc3151
csc315 2
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Find the exact value of the trig functions for the given angle
315
45
2-1
12
sec3151
sec315 2
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Find the exact value of the trig functions for the given angle
315
45
2-1
1
1cot 315
1
cot 315 1
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Find the exact value of the trig functions for the given angle
5
6
Quadrant II
306
3
12
5sin
6
5cos
6
5tan
6
5csc
6
5sec
6
5cot
6
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Find the exact value of the trig functions for the given angle
5
6
306
3
12
5 1sin
6 2
5 3cos
6 2
5 3tan
6 3
5csc 2
6
5 2 3sec
6 3
5cot 3
6
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The angle measures that place the terminal ray on one of the axes.
Degrees - 0⁰, 90⁰, 180⁰, 270⁰, 360⁰, …
Radians – 0, π/2, π, 3π/2, 2π, …
For these, draw and label a point 1 unit from the origin to find the values of the trigonometric functions.
Quadrantal Angles
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(-1,0)
r=1
sin
cos
tan
csc
sec
cot
01
11
01
0
1
0
10
11
10
1
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Assignmentp. 384 # 51 - 66 multiples of 3
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Using your Calculator… Set MODE according to how the angle is
measured (“degrees” or “radians”)
Use the SIN, COS, or TAN keys
Close parentheses after the angle measure
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cos14
cos14 0.97
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10sin
10sin 0.31
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csc37
csc37 1.66
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csc37
csc37 1.66
Alternative
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If (-5,12) is on the terminal side, find the exact value of the six trig functionsQuadrant II
(-5,12)
-5
12 13
sin
cos
tan
csc
sec
cot
1213
513
12 125 5
1312
13 135 5
512
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If (2,-1) is on the terminal side, find the exact value of the six trig functionsQuadrant IV
(2,-1)
-1
2
sin
cos
tan
csc
sec
cot
55
2 55
12
52
5
2
5
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Assignmentp. 384 # 69 - 81 multiples of 3, 83 - 92