Sketching sine, cosine and tangent

Sine and cosine have period 360° and range −1 to 1. Sine starts at zero and rises; cosine starts at one. Mark the values at 0°, 90°, 180°, 270° and 360°, then draw a smooth curve. The graphs continue to negative angles and to angles greater than a full revolution.

Tangent has period 180° and is undefined at 90° + 180°k for any integer k. Draw separate branches between these vertical asymptotes; never join a curve across an asymptote. For sin(bx), the period is 360°/|b| when b is nonzero. An input shift moves the key x-values, while multiplying the output changes the vertical scale.

Worked example

Sketch y = sin(2x) for 0° ≤ x ≤ 360°.

1. The period is 360°/2 = 180°.
2. Zeros occur at x = 0°, 90°, 180°, 270° and 360°.
3. The maxima are at 45° and 225°; minima are at 135° and 315°.

Answer: Two complete waves with range −1 to 1