← Back to Module 3

Module 3 Study Guide: Trig Functions of Any Angle

Trigonometry • Learn Without Walls

1. Coordinate Definition

sin θ = y/r   cos θ = x/r   tan θ = y/x   (r = √(x²+y²))

2. Reciprocal Identities

csc θ = 1/sin θ   sec θ = 1/cos θ   cot θ = 1/tan θ

3. Quotient Identities

tan θ = sin θ/cos θ    cot θ = cos θ/sin θ

4. Pythagorean Identities

sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = csc²θ

5. Even-Odd Properties

Even: cos(−θ) = cos θ, sec(−θ) = sec θ
Odd: sin(−θ) = −sin θ, tan(−θ) = −tan θ, csc(−θ) = −csc θ, cot(−θ) = −cot θ

6. Cofunction Identities

sin θ = cos(π/2 − θ)   cos θ = sin(π/2 − θ)   tan θ = cot(π/2 − θ)
sec θ = csc(π/2 − θ)   csc θ = sec(π/2 − θ)   cot θ = tan(π/2 − θ)

7. Strategy: Finding All Six from One

  1. Use Pythagorean identity to find a second value
  2. Apply sign from quadrant
  3. Use quotient identities for tan/cot
  4. Use reciprocal identities for csc/sec/cot