Transcript Document
Trigonometry Review
Angle Measurement
360 2 radians, so 180 radians
.
To convert from degrees to radians, multiply by
180
To convert from radians to degrees, multiply by
180
.
Special Angles
2
3
2
120
3
135
4
5 150
6
180
90
60
3
45
4
30
6
0
r=1
3 / 2 270
Special Angles - Unit Circle Coordinates
1
3
,
2
2
0,1
1 , 1
2
2
3π/4
2π/3
3
1
,
2
2
5π/6
1,0
1
3
,
2
2
π/2
π/3
π/4
π/6
0
π
3π/2
0 ,1
r=1
1 , 1
2
2
3
1
,
2
2
1,0
Trig Functions - Definitions
y
sin
r
r
csc
y
x
cos
r
r
sec
x
y
tan
x
x
cot
y
r
r
(x,y)
x y
2
2
Trig Functions - Definitions
opp
sin
hyp
adj
cos
hyp
opp
tan
adj
hyp
opp
adj
Trig Functions - Definitions
opp
sin
hyp
hyp
csc
opp
adj
cos
hyp
hyp
sec
adj
opp
tan
adj
adj
cot
opp
Trig Functions
Signs by quadrants
sin, csc positive
tan, cot positive
all functions positive
cos, sec positive
Trig Identities
Reciprocal
1
csc
sin
1
sec
cos
1
cot
tan
Quotient
sin
tan
cos
cos
cot
sin
Trig Identities
Pythagorean
sin cos 1
2
2
tan 1 sec
2
2
1 cot csc
2
2
Trig Identities
Double Angle
sin2 2 sin cos
cos 2 cos sin
2
2
2 cos 1
2
1 2 sin2
Inverse Trig Functions
y sin1 x arcsin x is equivalent to x sin y
y cos1 x arccosx is equivalent to x cos y
Solving Trig Equations
Use algebra, then inverse trig functions or knowledge
of special angles to solve.
1
example: if sin
2
0 2