Math 112 Recitation Assignment Name: _________________________________ Week 7 Group Members: Recitation Time:____________ _______________________________________

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1. Solving Trig Equations:

For each equation below:

(I) Find all solutions; round answers to 3 decimal

places when an exact answers cannot be found

using the unit circle.

(II) Find the solutions on the indicated interval.

(III) Check your answers.

a. 2 cot 𝑡 + 1 = −1 b. 8 cos 2𝑡 − 2 = 6

(I) All solutions: (I) All solutions:

(II) Solutions on [0, 2𝜋): (II) Solutions on [0, 2𝜋):

(III) Check: (III) Check:

HINT: on parts (c) and (d), it may be helpful to use fundamental identities.

c. 𝑠𝑒𝑐! 𝑥 − tan 𝑥 = 7 d. sin 𝑥 + csc 𝑥 = 2

(I) All solutions: (I) All solutions:

(II) Solutions on 0° ≤ 𝑥 ≤ 180°: (II) Solutions on [0, 2𝜋):

(III) Check: (III) Check:

2. Using Graphs and Sum /Difference Identities to Verify Identities:

a. Describe the transformations of the graph of 𝑦 = cos  (𝑡) needed to obtain the graph of each function below. Then, sketch a graph of each function.

𝑦 = − cos(𝑡) 𝑦 = cos(𝑡 + 𝜋)

What do you notice?

b. Recall that the Sum Identity for cosine is:

cos 𝐴 + 𝐵 = cos 𝐴 cos 𝐵 − sin 𝐴 sin 𝐵

Use the Sum Identity to verify the following identity symbolically.

− cos(𝑡) = cos(𝑡 + 𝜋)

-2π -π 0 π 2π

-1

1

-2π -π 0 π 2π

-1

1

2. Using Sum/Difference Identities to Evaluate Trig Expressions:

Given:

• cos 𝜃 = − !!"

and cos 𝛾 = !!!"

• 𝜃 is in quadrant III • 𝛾 is in quadrant I

Find:

• sin 𝜃 + 𝛾 • cos 𝜃 + 𝛾 • The quadrant containing 𝜃 + 𝛾