# Chapter 5.1 Fundamental Identities

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```					            Chapter 5.1
Fundamental Identities
Learning Target: I can use the fundamental
identities to simplify trigonometric expressions
and solve trigonometric equations.
Basic Trig Identities
•   Csc (θ) = 1/sin(θ)
•   Sec (θ) = 1/cos(θ)
•   Cot(θ) = 1/tan(θ)
•   Sin(θ) = 1/csc(θ)
•   Cos(θ) = 1/sec(θ)
•   Tan(θ) = 1/cot(θ)
•   Tan(θ) = sin(θ)/cos(θ)
•   Cot(θ) = cos(θ)/sin(θ)
Pythagorean Identities
• (sin t)2 + (cos t)2 = 1

• (cos t)2/(cos t)2 + (sin t)2/(cos t)2 = 1/(cos t)2
→ 1 + (tan t)2 = (sec t)2

(cos t)2/(sin t)2 + (sin t)2/(sin t)2 = 1/(sin t)2
→ (cot t)2 + 1 = (csc t)2
Cofunction Identities
Odd-Even Identities
sin (–x) = –sin x
cos (–x) = cos x
tan (–x) = –tan x
csc (–x) = –csc x
sec (–x) = sec x
cot (–x) = –cot x
Example
• Simplify by expanding and using identities.
• (sec(x) + 1)(sec(x) - 1)/(sin2(x))
Example
• Simplify by combining fractions and using
identities.
• Cos(x)/(1-sin(x)) – sin(x)/cos(x)
Example
• Find all values of x in the interval [0,2П]
that solve cos3(x)/sin(x) = cot(x)
Homework

Pg. 451
# 3 – 54 every 3rd

```
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