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# Finding the Equations of Trigonometric Functions - Word Problems (Degrees)

1. 1
Find two equations (using cosine and sine) to model the following:

A mass on the end of a spring is at rest 60 cm above the ground. it is pulled down 40 cm and released at time $t=0$. It takes 2 seconds for the mass to return to the low position.
2. 2
Find two equations (using cosine and sine) to model the following:

A mass on the end of a spring is at rest 80 cm above the ground. it is pulled down 30 cm and released at time $t=0$. It takes 2.4 seconds for the mass to return to the low position.
3. 3
Find an equation for the following:

A mass on the end of a spring is at rest 120 cm above the ground. it is pulled down 50 cm and released at time $t=0$. It takes 6 seconds for the mass to return to the low position.

Use the equation to find:
a) The height of the mass after 4 seconds.
b) The first four times the mass to reached 95 cm.

Good test question !

The rest of these questions require you to solve trigonometric equations. (CAST and unit circle)
4. 4
Find an equation for the following:

A mass on the end of a spring is at rest 200 cm above the ground. it is pulled down 85 cm and released at time $t=0$. It takes 12 seconds for the mass to return to the low position.

Use the equation to find:
a) The height of the mass after 5 seconds.
b) The first four times the mass reached 240 cm.
5. 5
A ferris wheel has a diameter of 24 metres and rotates every 16 seconds. the bottom of the wheel is 2 metres above the ground. (assume you start the ride when you get on).

a) Sketch a graph
b) Find the equation for the riders height above the ground.
c) How high above the ground are you after 18 s?
d) Find the first four times when you are 17 metres above the ground.

Good test question !
6. 6
A ferris wheel has a diameter of 14.5 metres and rotates every 20 seconds. the bottom of the wheel is 1.5 metres above the ground. (assume you start the ride when you get on).

a) Sketch a graph
b) Find the equation for the riders height above the ground.
c) How high above the ground are you after 25 s?
d) Find the first four times when you are 14 metres above the ground.
7. 7
Day of the yearsunset time
17220 h
35516 h
A city in the northern hemisphere has the following sunset times for the given days of the year.

a) Find an equation for the time of sunset for any day of the year.
b) Find the sunset time for the 50th day.
c) What day(s) will the sun set at 19 h?

Good test question !
8. 8
Day of the yearHours of sunlight
17216.7 h
3559.1 h
A city in the northern hemisphere has the following hours of sunlight for the given days of the year.

a) Find an equation for the hours of sunlight for any day of the year.
b) Find the number of hours of sunlight for the 70th day.
c) What day(s) will have 15 hours of sunlight?

Good test question !
9. 9
The water depth at 08:00h is 7 m(low tide) and the depth at 14:00h is 21 m (high tide).

a) Sketch the function.
b) Find an equation for the water depth as a function of time.
c) Find a time when the depth is 16 metres.

( trigonometry / trig )

$$e=mc^2$$