1. Important Angles

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

3. 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
(0,1) π/2
(1,0)
0, 2π
(–1,0) π
(0,–1) 3π/2
π/ π π/ π

4. 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
(0,1) π/2
(1,0)
0, 2π
(–1,0) π
(0,–1) 3π/2
π/ π π/ π

5. sin and cos of nπ/2
sin (0) = cos (0) = sin (π/2) = cos (π/2) = sin (π) = cos (π) = sin (3π/2) = cos (3π/2) = 1 –1 1 –1
(0,1) π/2
(1,0)
0, 2π
(–1,0) π
(0,–1) 3π/2
π/ π 3π/2 2π
π/ π 3π/2 2π

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

7. Don’t memorize sin π/3, cos π/6, tan π/4, etc
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 2x
x√3
π/2
π/4 x
π/2
π/3

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

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

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

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