Download Evaluating Trigonometric Functions (Precalculus Review 3)

Evaluating Trigonometric
Functions
(Precalculus Review 3)
September 10th, 2015
I. SOH CAH TOA
opp y
sin q =
=
hyp r
adj x
cos q =
=
hyp r
opp y
tan q =
=
adj x
hyp r
csc q =
=
opp y
hyp r
secq =
=
adj x
adj x
cot q =
=
opp y
II. Special Right Triangles
x
x 2
45°
x
x
60°
2x
45°
30°
x 3
*To make things simple, use x=1 when evaluating
trig ratios.
45°
2
1
1
60°
2
30°
45°
1
3
III. Radian Measure
3p
5p
2p
4
3
p
2
p
p
6
p
3
6
p
4
p
4
6
p
3
p
7p
0;2p
11p
6
5p
4
4p
3
3p
2
5p
3
7p
4
6
180°
=
= 30°
6
180°
=
= 45°
4
180°
=
= 60°
3
Ex. 1: Evaluate each.
a) tan
p
6
4p
b)csc
3
3p
c)cos
4
5p
d)cot
6
5p
e)sin
3
*To remember which functions are positive in each
quadrant:
Quad II
Students
(sin)
Quad I
All
(all)
Quad III
Take
(tan)
Quad IV
Calculus
(cos)
IV. Quadrant Angles
*Use points on the unit circle to evaluate trig
functions for quadrant angles.
p
2
p
0;2p
3p
2
Ex. 2: Evaluate each.
3p
a)cos
2
b)csc p
c)sin 2p
d)cot
p
2
V. Trigonometric identities
Reciprocal Identities:
1
1
1
sin q =
,cosq =
, tanq =
cscq
secq
cot q
1
1
1
cscq =
,secq =
,cot q =
sin q
cosq
tanq
Quotient Identities:
sinq
cosq
tanq =
,cot q =
cosq
sinq
Pythagorean Identities:
sin 2 q + cos 2 q = 1
1+ tan 2 q = sec 2 q
1+ cot 2 q = csc 2 q
Double Angle Identity:
sin2q = 2sinq cosq
VI. Graphs of Trigonometric
Functions
y = sin x
D : ( -¥,¥ )
R :[-1,1]
period = 2p
y = cos x
D : ( -¥,¥ )
R :[-1,1]
period = 2p
y = tan x
period = p
D: All real
numbers except
x = p 2 + np
R : ( -¥,¥ )
Vertical Asymptotes:
x = p 2 + pn