Angle and Radian Measure
Circumference
Degrees to Radians
Multiply by
72°
𝜋
180°
52.4°
More. . . .
120°
148°
Radians to Degrees
Multiply by
3𝜋
18
180°
𝜋
𝜋
5
More. . .
𝜋
4
1.4
Remember?
The side lengths of a 45-45-90 triangle are
always in the ratio:
45
90
45
More Remembering. . .
The side lengths of a 30-60-90 triangle are
always in the ratio:
30
90
60
Trig Ratios
Let 𝜃 be an acute angle in the right ∆𝐴𝐵𝐶
A
𝜃
C
B
𝑠𝑖𝑛𝜃 =
cscθ =
𝑐𝑜𝑠𝜃 =
𝑠𝑒𝑐𝜃 =
𝑡𝑎𝑛𝜃 =
𝑐𝑜𝑡𝜃 =
Find all six trig functions for an angle
of 60°
60
𝑠𝑖𝑛𝜃 =
cscθ =
𝑐𝑜𝑠𝜃 =
𝑠𝑒𝑐𝜃 =
𝑡𝑎𝑛𝜃 =
𝑐𝑜𝑡𝜃 =
Find all six trig ratios for the angle 𝜃
using the triangle below
10
𝑠𝑖𝑛𝜃 =
cscθ =
𝑐𝑜𝑠𝜃 =
𝑠𝑒𝑐𝜃 =
𝑡𝑎𝑛𝜃 =
𝑐𝑜𝑡𝜃 =
5
𝜃
Using One Trig Ratio to Find Them All:
If we are given one of the trig ratios, we can use
that to find the other 5. Steps:
1. Sketch a triangle
2. Label two sides using the given ratio
3. Use the Pythagorean Theorem to find
missing side
4. Write the remaining 5 ratios
Find all trig ratios
3
𝑠𝑖𝑛𝜃 =
7
Another one. . .
3
𝑐𝑜𝑡𝜃 =
4