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MA1310: Week 3 Graphs of Sine and Cosine Functions

This lab requires you to:

· Use the definitions of trigonometric functions of any angle.

· Use the signs of the trigonometric functions.

· Find reference angles.

· Use reference angles to evaluate trigonometric functions.

Trigonometric functions are used to model data and a variety of physical phenomena such as astronomy, surveying, highway design, GPS, and aerial photography. Click here to refer to the basics of trigonometry and answer the following questions to complete this lab:

1. Find the exact value of:

a. sin 300°

b. tan (405°) (Hint: 405° = 360° + 45°)

c. cot ( (Hint: )

2. If sin θ < 0 and tan θ < 0, then in which quadrant does θ lie?

3. Find the exact value of sin θ, if cos θ = and θ lies in quadrant IV.

4. Define the following for a sinusoidal graph in general.

a. Amplitude

b. Period

c. Phase Shift

5.

Given the function

a. Find the amplitude.

b. Find the period.

c. Identify the correct graph from the following choices:

i.

y

x

5

-5

1

-1

3

-3

ii.

y

x

5

-5

1

-1

3

-3

iii.

y

x

5

-5

1

-2

3

-3

6.