Solving Trig Equations: 4 More Solutions to Find

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The discussion centers on solving the trigonometric equation cos^2(3x) = 1 for all values of the variable within the first positive rotation. The initial approach incorrectly applied arccos, leading to confusion about the number of solutions. The correct interpretation reveals that cos(3x) can equal ±1, indicating multiple solutions. Participants clarify that the equation can yield four distinct solutions based on the periodic nature of the cosine function. The exchange ultimately aids in understanding the correct method to find all solutions.
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The question is Solve the trig equation for all values of the variable in the first positive rotation.

Problem cos^2 3x = 1

Heres how I attempted to solve the equation

3x = arccos (1)^2

1/3 arccos 1

cos = 0 & 180

However, on the test, the professor stated there were 4 more solutions & I'm having trouble trying to figure them out. What more do I need to do?
 
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kuahji said:
3x = arccos (1)^2
This is wrong.cos2(3x) = 1
<=> cos 3x = +- 1
Can you do the rest?
 
Yes, thank you. I see what I did now & this helps.
 

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