1. No category

Pre-Calculus 139
θ Deg
θ Rad
W (θ )
sin(θ )
cos(θ )
tan(θ )
0˚
0
(1,0)
1
0
30˚
π
3
2
3
3
45˚
π
2
2
2
2
1
60˚
π
⎛ 3 1 ⎞
⎜
⎟
⎜ 2 , 2 ⎟
⎝
⎠
⎛ 2 2 ⎞
⎜
⎟
⎜ 2 , 2 ⎟
⎝
⎠
⎛ 1 3 ⎞
⎜ ,
⎟
⎜ 2 2 ⎟
⎝
⎠
0
1
2
3
2
1
2
3
90˚
π
1
0
∞
6
4
3
2
(0,1)
Right Triangle Definitions
opp
1.
sin(θ )=
hyp
adj
2.
cos(θ )=
hyp
opp
3.
tan(θ )=
adj
adj
4.
cot(θ )=
opp
hyp
5.
sec(θ )=
adj
hyp
6.
csc(θ )=
opp
Complement Relationships
⎛ π
⎞
1.
sin ⎜ − θ ⎟ = cos(θ )
⎝ 2
⎠
⎛ π
⎞
2.
cos⎜ − θ ⎟ = sin (ϑ )
⎝ 2
⎠
⎛ π
⎞
3.
tan ⎜ − θ ⎟ = cot(θ )
⎝ 2
⎠
⎛ π
⎞
4.
cot⎜ − θ ⎟ = tan (θ )
⎝ 2
⎠
⎛ π
⎞
5.
sec⎜ − θ ⎟ = csc(θ )
⎝ 2
⎠
⎛ π
⎞
6.
csc⎜ − θ ⎟ = sec(θ )
⎝ 2
⎠
Reciprocal Identities
1
1.
sin (θ ) =
csc(θ )
1
2.
cos(θ ) =
sec(θ )
1
3.
tan (θ ) =
cot(θ )
1
4.
cot(θ ) =
tan (θ )
1
5.
sec(θ ) =
cos(θ )
1
6.
csc(θ ) =
sin (θ )
Quotient Identities
sin (θ )
1.
tan(θ ) =
cos(θ )
cos(θ )
2.
cot(θ ) =
sin (θ )
Pythagorean Identities
1.
sin 2 (θ ) + cos 2 (θ ) = 1
2.
1 + tan 2 (θ ) = sec 2 (θ )
3.
1 + cot 2 (θ ) = csc 2 (θ )
To confirm a proposed Trigonometric Identity, we work with only one side of the equation and make it look
like the other side:
Prove: sec x cot x = csc x
Work on the left side:
1 cos x
1
=
= csc x QED
⋅
cos x sin x sin x
Assignment 139 – Page 284, #’s 6, 36, 38, 45, 50, 56, 79, 80, 81, 82, 83