Radians, the unit circle and trigonometric identities

Learning objectives

Convert between degrees and radians, and calculate arc lengths and sector areas using radian measure

Define cos θ and sin θ as the coordinates of a point on the unit circle and tan θ as sin θ / cos θ, and use the signs of the ratios in each quadrant

Recall the exact values of sin, cos and tan of 0, π/6, π/4, π/3 and π/2 and their multiples, and use symmetry to find the ratios of related angles without a calculator

Use the Pythagorean identity cos²θ + sin²θ = 1 and the double angle identities for sine and cosine to simplify expressions and find exact values

Apply the ambiguous case of the sine rule to decide when two different triangles are possible and find both solutions