Trigonometric Functions on a Unit Circle Flashcards

Sine Function Values

• sin(0) = 0
• sin(π/6) = 1/2
• sin(π/4) = √2/2
• sin(π/3) = √3/2
• sin(π/2) = 1
• sin(2π/3) = √3/2
• sin(3π/4) = √2/2
• sin(5π/6) = 1/2
• sin(π) = 0
• sin(7π/6) = -1/2
• sin(5π/4) = -√2/2
• sin(4π/3) = -√3/2
• sin(3π/2) = -1
• sin(5π/3) = -√3/2
• sin(7π/4) = -√2/2
• sin(11π/6) = -1/2
• sin(2π) = 0

Cosine Function Values

• cos(0) = 1
• cos(π/6) = √3/2
• cos(π/4) = √2/2
• cos(π/3) = 1/2
• cos(π/2) = 0
• cos(2π/3) = -1/2
• cos(3π/4) = -√2/2
• cos(5π/6) = -√3/2
• cos(π) = -1
• cos(7π/6) = -√3/2
• cos(5π/4) = -√2/2
• cos(4π/3) = -1/2
• cos(3π/2) = 0
• cos(5π/3) = 1/2
• cos(7π/4) = √2/2
• cos(11π/6) = √3/2
• cos(2π) = 1

Tangent Function Values

• tan(0) = 0
• tan(π/6) = √3/3
• tan(π/4) = 1
• tan(π/3) = √3
• tan(π/2) = undefined
• tan(2π/3) = -√3
• tan(3π/4) = -1
• tan(5π/6) = -√3/3
• tan(π) = 0
• tan(7π/6) = √3/3
• tan(5π/4) = 1
• tan(4π/3) = √3
• tan(3π/2) = undefined
• tan(5π/3) = -√3
• tan(7π/4) = -1
• tan(11π/6) = -√3/3
• tan(2π) = 0

General Notes

• Sine values range from -1 to 1.
• Cosine values also range from -1 to 1.
• Tangent values can be undefined for angles where cosine is zero.
• Angles are often expressed in radians, which are essential for calculations in trigonometry, especially on the unit circle.