Grades Algebra II & Trigonometry Trigonometric FunctionsUnit Circle & Radian Measure

Unit Circle & Radian Measure

🌊 Trigonometric Functions

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Unit Circle & Radian Measure

Define trig functions via the unit circle and convert between degrees and radians.

The unit circle has radius 1 centered at the origin. For any angle θ (measured from the positive x-axis), the terminal point on the unit circle has coordinates (cos θ, sin θ). Radian measure defines the angle by the arc length it subtends on the unit circle.

\theta_{\text{rad}} = \theta_{\text{deg}} \times \frac{\pi}{180} \qquad 360^\circ = 2\pi \text{ rad}

Key Unit Circle Values

0° (0): (1, 0) → cos 0 = 1, sin 0 = 030° (π/6): (√3/2, 1/2)45° (π/4): (√2/2, √2/2)60° (π/3): (1/2, √3/2)90° (π/2): (0, 1) → cos 90° = 0, sin 90° = 1

Memorizing these values allows you to evaluate trig functions exactly.

\cos\frac{\pi}{3} = \frac{1}{2} \qquad \sin\frac{\pi}{3} = \frac{\sqrt{3}}{2} \qquad \tan\frac{\pi}{3} = \sqrt{3}

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Remember This!

Use the mnemonic "All Students Take Calculus" to remember signs in each quadrant: All positive (Q1), Sine positive (Q2), Tangent positive (Q3), Cosine positive (Q4).

✏️ Try It!

What is cos(3π/2)?

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⭕Unit Circle Converter

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