Important Angles Learn to Love Radians 0 45

Important Angles

Learn to Love Radians 0° = 45° = 90° = 135° = 180° = 225° = 270° = 315° = 360° = 0 Radians π/4 Radians π/2 Radians 3π/4 Radians π Radians 5π/4 Radians 3π/2 Radians 7π/4 Radians 2π Radians 30° = π/6 Radians 60° = π/3 Radians

sin (nπ/2) where n = any integer To find the sine of intervals of π/2 (90°) you need to either use the unit circle where sin x is the y-value or graph y = sin x 1 1 (0, 1) π/2 -1 (– 1, 0) π 0 0 (1, 0) 0, 2π 0 -1 1. 5707963267949 3. 1415926535898 4. 7123889803847 6. 28318530717958 1 -1 (0, – 1) 3π/2 0 0 π/2 π 3π/2 2π

cos (nπ/2) where n = any integer To find the sine of intervals of π/2 (90°) you need to either use the unit circle where sin x is the x-value or graph y = cos x 1 1 (0, 1) π/2 -1 (– 1, 0) π 0 0 (1, 0) 0, 2π 0 -1 1. 5707963267949 3. 1415926535898 4. 7123889803847 6. 28318530717958 1 -1 (0, – 1) 3π/2 0 0 π/2 π 3π/2 2π

sin and cos of nπ/2 0 sin (0) = sin (π/2) = 1 0 sin (π) = sin (3π/2) = – 1 cos (0) = cos (π/2) = cos (π) = cos (3π/2) = 1 0 1 1 (0, 1) π/2 -1 0 1. 5707963267949 3. 1415926535898 4. 7123889803847 6. 28318530717958 (– 1, 0) π 0 0 1 0 – 1 0 (1, 0) 0, 2π 1 0 0 1. 5707963267949 3. 1415926535898 4. 7123889803847 6. 28318530717958 (0, – 1) 3π/2 -1 -1 0 π/2 π 3π/2 2π

6 Trig Functions How do you calculate the each trig function sin θ = opposite / hypotenuse cos θ = adjacent / hypotenuse tan θ = opposite / adjacent sec θ = hypotenuse / adjacent csc θ = hypotenuse / opposite cot θ = adjacent / opposite

Don’t memorize sin π/3, cos π/6, tan π/4, etc. Memorize the 2 triangles and then use your knowledge of trig to figure out sin, cos, tan, etc. π/4 π/6 x 2 x x√ 3 x√ 2 π/4 x π/2 π/3

π/4 -π/2 Triangle sin (π/4) = π/4 x π/2 x x√ 2 cos (π/4) = π/4 tan (π/4) = sec (π/4) = csc (π/4) = cot (π/4) =

π/6 -π/3 -π/2 Triangle sin (π/6) = π/6 cos (π/6) = 2 x x√ 3 tan (π/6) = sec (π/6) = π/2 x π/3 csc (π/6) = cot (π/6) =

π/6 -π/3 -π/2 Triangle sin (π/3) = π/6 cos (π/3) = 2 x x√ 3 tan (π/3) = sec (π/3) = π/2 x π/3 csc (π/3) = cot (π/3) =

Inverse Trig Functions Working backwards, find the angle Remember, sin-1 x means sin of ___ angle = x sin-1 0 = sec-1 1 = sin-1 0. 5 = sec-1 √ 2 = sin-1 1 = csc-1 √ 2 = cos-1 1 = tan-1 0 = cos-1 0. 5 = tan-1 1 = cos-1 0 = tan-1 √ 3 =