Trigonometry on the Unit Circle

Sine and cosine have period 360°; tangent has period 180°. sin(−α) = −sin α. Sine is positive in quadrants I and II and negative in III and IV; cosine is also negative in III. Special values: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2.

Sine and cosine have period 360°; tangent has period 180°. sin(−α) = −sin α. Sine is positive in quadrants I and II and negative in III and IV; cosine is also negative in III. Special values: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2.

Sine and cosine have period 360°; tangent has period 180°. sin(−α) = −sin α. Sine is positive in quadrants I and II and negative in III and IV; cosine is also negative in III. Special values: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2.

The period of the tangent function is 180°. Therefore, adding or subtracting any integer multiple of 180° does not change the tangent value.

Rule: tan(α + 180° · k) = tan α, where k is an integer.

1. Notice that 180° · k has been added to the angle.
2. This is a whole number of tangent periods, so that part may be removed.
3. The expression becomes tan α.

Thus, keep the tangent function and the original angle that appears before the added multiple of 180°.

Sine and cosine have period 360°; tangent has period 180°. sin(−α) = −sin α. Sine is positive in quadrants I and II and negative in III and IV; cosine is also negative in III. Special values: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2.

For an angle in radians, arc length is radius times angle. Multiply the coefficients exactly and retain π.

Sine and cosine have period 360°; tangent has period 180°. sin(−α) = −sin α. Sine is positive in quadrants I and II and negative in III and IV; cosine is also negative in III. Special values: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2.

Use sin² α + cos² α = 1. Select the cosine sign from the condition, then use tan α = sin α / cos α.

arcsin s returns the principal angle in [−90°, 90°], while arccos s returns one in [0°, 180°]. The input must be between −1 and 1. Find the angle in the appropriate interval whose sine or cosine equals s.

Tangent has period 180°. Add or subtract whole periods to obtain a familiar angle. Use its odd symmetry when needed.