4.8 Solving Problems with Trigonometry

Quick Review

1. Solve for a.

a

3

23º

Quick Review

2. Find the complement of 47o.

3. Find the supplement of 47o.

4. State the bearing that describes the direction NW (northwest).

5. State the amplitude and period of the sinusoid 3cos2(x 1).

What you’ll learn about• More Right Triangle Problems• Simple Harmonic Motion

… and why

These problems illustrate some of the better-known applications of trigonometry.

Angle of Elevation, Angle of Depression

• An angle of elevation is the angle through which the eye moves up from horizontal to look at something above.

•An angle of depression is the angle through which the eye moves down from horizontal to look at something below.

The angle of depression from the top of a lighthouse 130 feet tall to a boat in the sea is 6 degrees. Find the distance that the boat is from the lighthouse.

A large helium-filled Spongebob has 2 cables attached from Spongebob to the ground. One cable makes an angle of 48 degrees from the ground and the other 40 degrees. If the cables are attached to the ground 10 feet from each other, how high is Spongebob?

From the top of a 100 ft tall building a man observes a car moving toward the building. If the angle of depression of the car changes from 22 degrees to 46 degrees during the period of observation, how far does the car travel?

Simple Harmonic Motion

A point moving on a number line is in if its

directed distance from the origin is given by either

sin or cos , where and are real numbers and 0.

The motion has

d

d a t d a t a

simple harmonic motion

frequency / 2 , which is the number of

oscillations per unit of time.

Calculating Harmonic Motion

A mass oscillating up and down on the bottom of a spring (assuming perfect elasticity and no friction or air resistance) can be modeled as harmonic motion. If the weight is displaced a maximum of 4 cm, find the modeling equation if it takes 3 seconds to complete one cycle.

Try these and turn in!

• Pg. 432-433 #1, 3, 11, 27, 29