5.2 Trigonometric Functions
Sine, Cosine, Tangent, Cosecant, Secant, Cotangent
ry
x
siny
r
Sine
ry
x
cosx
r
Cosine
ry
x
tany
x
Tangent
sintan
cos
ry
x
cscr
y
Cosecant
1csc
sin
ry
x
secr
x
Secant
1sec
cos
ry
x
cotx
y
Cotangent
coscot
sin
Review - Special Right Triangles
21
1
45 30
3
2 1
60
32
1
454
603
306
You MUST know these!
Find the exact value of the trig functions for the given angle
315 Quadrant IV
Find the exact value of the trig functions for the given angle
315
Reference Angle 45⁰
Find the exact value of the trig functions for the given angle
315
45
Find the exact value of the trig functions for the given angle
315
45
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
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
Find the exact value of the trig functions for the given angle
315
45
2-1
1
1tan315
1
tan315 1
Find the exact value of the trig functions for the given angle
315
45
2-1
12
csc3151
csc315 2
Find the exact value of the trig functions for the given angle
315
45
2-1
12
sec3151
sec315 2
Find the exact value of the trig functions for the given angle
315
45
2-1
1
1cot 315
1
cot 315 1
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
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
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
(-1,0)
r=1
sin
cos
tan
csc
sec
cot
01
11
01
0
1
0
10
11
10
1
Assignmentp. 384 # 51 - 66 multiples of 3
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
cos14
cos14 0.97
10sin
10sin 0.31
csc37
csc37 1.66
csc37
csc37 1.66
Alternative
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
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
Assignmentp. 384 # 69 - 81 multiples of 3, 83 - 92