Pre-Calculus
148
Recall the following fundamental trigonometric identities.
Complement Formulas
⎛ π
⎞
sin ⎜ − x ⎟ = cos x
⎝ 2
⎠
⎛ π
⎞
cos ⎜ − x ⎟ = sin x
⎝ 2
⎠
⎛ π
⎞
tan ⎜ − x ⎟ = cot x
⎝ 2
⎠
⎛ π
⎞
cot ⎜ − x ⎟ = tan x
⎝ 2
⎠
⎛ π
⎞
sec ⎜ − x ⎟ = csc x
⎝ 2
⎠
⎛ π
⎞
csc ⎜ − x ⎟ = sec x
⎝ 2
⎠
Even vs Odd Trig Functions
sin(-x) = -sin x
Sine is an Odd Function.
cos(-x) = cos x
Cosine is an Even Function.
tan(-x) = -tan x
Tangent is an Odd Function.
cot(-x) = -cot x
Cotangent is an Odd Function.
sec(-x) = sec x
Secant is an Even Function.
csc(-x) = -csc x
Cosecant is an Odd Function.
Quotient & Reciprocal Identities
sin x/cos x = tan x
cos x/sin x = cot x
1/sec x = cos x
1/csc x = sin x
1/tan x = cot x
Pythagorean Trigonometric Identities
sin2x + cos2x = 1
1 – sin2x = cos2x
1 – cos2x = sin2x
tan2x + 1 = sec2x
cot2x + 1 = csc2x
Pre-Calculus 1 Assignment 148 Friday, December 18, 2015 Hour
Name
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Use the fundamental identities to simplify the expressions.
1.
cot x sin x
2.
cos B tan B
3.
sin θ (cscθ − sin θ )
4.
sec2x(1 - sin2x)
5.
csc x
cot x
6.
secθ
cscθ
7.
sec a •
8.
sin a
tan a
tan 2 θ
sec 2 θ
9.
⎛ π
⎞
sin ⎜ − x ⎟ csc x
⎝ 2
⎠
10.
⎛ π
⎞
cot⎜ − x ⎟ cos x
⎝ 2
⎠
11.
cos 2 y
1 − sin y
12.
1
cot 2 x + 1