Solving Trig Equations: 4 More Solutions to Find

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SUMMARY

The discussion centers on solving the trigonometric equation cos²(3x) = 1. The initial approach incorrectly used arccos(1) leading to a misunderstanding of the solutions. The correct interpretation reveals that cos(3x) = ±1, which indicates multiple solutions within the first positive rotation. The professor confirmed that there are four additional solutions to consider, emphasizing the need for a comprehensive understanding of trigonometric identities and periodicity.

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kuahji
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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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