Opposite = the length of the side opposite θ
Adjacent = the length of the side adjacent to θ
Hypotenuse = the length of the hypotenuse

Example of a Trigonometric Triangle

- Sine, Cosine, and Tangent can be used when finding side measurements of right triangles.
- When x and a side measurement are given, you can determine which formula you will use.

Sample Problems using above triangle:
1. What is the hypotenuse (H) measurement when x = 60° and O = 10in.?

sin(x) = O/H

sin(60°) = O/H

sin(60°) = 10in./H

H x sin(60°) = 10in.

H = 10in./sin(60°)

H = 11.55in.

2. What is the adjacent (A) measurement when x = 21° and H = 30ft.?

cos(x) = A/H

cos(21°) = A/H

cos(21°) = A/30ft.

30ft. x cos(21°) = A

A = 28.00ft.

3. What is the opposite (O) measurement when x= 5° and A= 27cm.?

tan(x)= O/A

tan(5°) = O/A

tan(5°) = O/27cm.

27cm. x tan(5°) = O

O = 2.36cm.

Special Triangles to Remember (These will make SOCAHTOA easier and faster to find) Fun Ways to Help Remember Sine, Cosine, andTangent

the old Indian Chief: SOCAHTOA

oh heck, another hour of algebra!

oscar had aheap of apples

Sines, Cosines, and Tangents of Special Angles

sin 30˚ = sin π/6 = ½ sin 45˚ = sin π/4 = √2/2 sin 60˚ = sin π/3 = √3/2

cos 30˚ = cos π/6 = √3/2 cos 45˚ = cos π/4 = √2/2 cos 60˚ = cos π/3 = ½

tan 30˚ = tan π/6 = √3/3 tan 45˚ = tan π/4 = 1 tan 60˚ = tan π/3 = √3

Practice Problems:

Use above triangle for practice problems.
Find the exact values of the six trigonometric functions for the triangle.

## Sine= Opposite/Hypotenuse

## Cosine= Adjacent/Hypotenuse

## Tangent= Opposite/Adjacent

Opposite = the length of the side opposite θAdjacent = the length of the side adjacent to θ

Hypotenuse = the length of the hypotenuse

- Sine, Cosine, and Tangent can be used when finding side measurements of right triangles.

- When x and a side measurement are given, you can determine which formula you will use.

Sample Problems using above triangle:

1. What is the hypotenuse (H) measurement when x = 60° and O = 10in.?

- sin(x) = O/H
- sin(60°) = O/H
- sin(60°) = 10in./H
- H x sin(60°) = 10in.
- H = 10in./sin(60°)
- H = 11.55in.

2. What is the adjacent (A) measurement when x = 21° and H = 30ft.?- cos(x) = A/H
- cos(21°) = A/H
- cos(21°) = A/30ft.
- 30ft. x cos(21°) = A
- A = 28.00ft.

3. What is the opposite (O) measurement when x= 5° and A= 27cm.?Special Triangles to Remember(These will make SOCAHTOA easier and faster to find)Fun Ways to Help Remember Sine, Cosine, andTangentheck,anotherhourofalgebra!hadaheapofapplesSines, Cosines, and Tangents of Special Anglessin 30˚ = sin π/6 = ½

sin 45˚ = sin π/4 = √2/2

sin 60˚ = sin π/3 = √3/2

cos 30˚ = cos π/6 = √3/2

cos 45˚ = cos π/4 = √2/2

cos 60˚ = cos π/3 = ½

tan 30˚ = tan π/6 = √3/3

tan 45˚ = tan π/4 = 1

tan 60˚ = tan π/3 = √3

Practice Problems:Use above triangle for practice problems.Find the exact values of the six trigonometric functions for the triangle.

1.A = 0.6, B = 0.8, C = 12.A = 1, B = 1, C = √2, a = 45°, b = 45°3.A = √3, B = 1, C = 24.A = 4, B = 3, C = 55.A = 6, B = 36.B = 2, C = 6