8-3

Trigonometry

Learning Goal

To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in

right triangles.

For the remainder of the year your calculator must be in

degree mode. All your answers will be wrong if it is not in degree

mode.

Get out your calculators now. Mr. Bradford will show you.

Do not copy.

Trigonometric Ratio

A ratio of the lengths of sides of a right triangle.

Do not copy.

Examples: sine, cosine and tangent.

Abbreviations: sin, cos and tan.

Some Old Horse Came A Hopping Through Our Alley

Some Old Horse

Sin Θ = oppositehypotenuse

Came A Hopping

Cos Θ = adjacenthypotenuse

Through Our Alley

Tan Θ =oppositeadjacent

Θ is the measure of an acute angle in a right triangle.

Step 1Label the Hypotenuse.(across from the right angle)

43˚

x

10

hyp

Step 2Put an arc over the angle that has a number or variable with a degree symbol.

43˚

x

10

hyp

Step 3Label the other side the arc touches: Adjacent.

43˚

x

10

hyp

adj

Step 4Label the remaining side: Opposite.

43˚

x

10

hyp

adj

opp

Step 5Decide if sin, cos or tan.

43˚

x

10

hyp

adj

opp

Step 6Create equation.

43˚

x

10

hyp

adj

opp

tan 43 = —10x

Step 7Solve.

tan 43 = —10x

Step 7Solve.

tan 43 = —10x

.9325 = —10x

Step 7Solve.

tan 43 = —10x

.9325 = —10x( )x( )x

Step 7Solve.

tan 43 = —10x

.9325 = —10x

.9325x = 10

( )x( )x

Step 7Solve.

tan 43 = —10x

.9325 = —10x

.9325x = 10

( )x( )x

.9325.9325

Step 7Solve.

tan 43 = —10x

.9325 = —10x

.9325x = 10

x = 10.7

( )x( )x

.9325.9325

Lets try another.

x˚

12

16

Lets try another.sin x = —12

16

Lets try another.sin x = —

sin x = .75

1216

Lets try another.sin x = —

sin x = .75

1216

sin-1(sin x) = sin-1.75

Lets try another.sin x = —

sin x = .75

1216

sin-1(sin x) = sin-1.75

Lets try another.sin x = —

sin x = .75

1216

sin-1(sin x) = sin-1.75

x = 48.6

Trigonometry Worksheet

5 Points: 100% Complete 4 Points: 80% Complete 3 Points: 60% Complete 2 Points: 40% Complete

1 Point: 20% Complete