Trigonometry

Trigonometry

1. Measures of Common Angles

   • sin0° = 0, cos0° = 1, tan0° = 0
   • sin30° = 1/2, cos30° = √3/2, tan30° = √3/3
   • sin45° = √2/2, cos45° = √2/2, tan45° = 1
   • sin60° = √3/2, cos60° = 1/2, tan60° = √3
   • sin90° = 1, cos90° = 0, tan90° = undefined

2. Pythagorean Theorem/Identitites

   • a² + b² = c²
   • tan²Ɵ + 1 = sec²Ɵ
   • 1 + cot²Ɵ = csc²Ɵ
   • sin²Ɵ + cos²Ɵ = 1

3. Signs of Angles in Quadrants

   • QI = All signs positive
   • QII = Only sine and its reciprocal are positive
   • QIII = Only tangent and its reciprocal are positive
   • QIV = Only cosine and its reciprocal are positive

4. Cofunctions

   • sinƟ = cosƟ (90°- Ɵ)
   • secƟ = cscƟ (90°- Ɵ)
   • tanƟ = cotƟ (90°- Ɵ)

5. Special Triangles

   • Right Triangles
     • sinƟ = opposite/hypotenuse
     • cosƟ = adjacent/hypotenuse
     • tanƟ = opposite/adjacent
   • 45°-45°-90° Triangles
   • 30°-60°-90° Triangles

6. Reciprocals

   • cscƟ = 1/sinƟ
   • secƟ = 1/cosƟ
   • cotƟ = 1/tanƟ