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Question

Find all exact solutions on the interval [0,2pi). If there is more than one answer, enter them as a comma separated list. If necessary, round to the nearest tenth.

1: 9sin(2𝑡)+2sin(𝑡)=0

2: 9cos(2𝑡)=9cos2(𝑡)−3

3: 2sin(2𝑡)=2cos(𝑡)

4: 4cos(2𝑡)=4sin(𝑡)

Answer 1

1) Answers are either exact or truncated decimals. They cannot be both.

2) Obtain a list of double angle formulae.

9 sin 2t + 2 sin t = 0

9 (2 sin t cos t) + 2 sin t = 0

18 sin t cos t + 2 sin t = 0

2 sin t (9 cos t + 1) = 0

sin t = 0 → t = 0, π

9 cos t + 1 = 0 → t = 1.682 radian

#2

set equal to 0, divide both sides by 3, convert cos 2t to 2cos² - 1, factor

#3

set equal to 0, divide both sides by 2, convert sin 2t to 2 sin t cos t, factor

#4

set equal to 0, divide both sides by 4, convert cos 2t to 1 - 2 sin² t, factor