How Do You Solve for Theta in Degrees When Given a Cosine Squared Equation?

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Discussion Overview

The discussion revolves around solving the equation 0.651 = cos²(theta) for theta in degrees. Participants explore various methods for handling the squared cosine function and the implications of taking square roots.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in solving the equation and seeks guidance on the correct approach.
  • Another suggests taking the square roots of both sides as a potential first step.
  • A third participant advises that after taking the square root, one should also consider taking the arc cosine of both sides.
  • One participant warns that simply taking the square root may not suffice, indicating the need to account for the negative square root to avoid losing information.
  • Another proposes treating the equation like a quadratic, suggesting that this method would not lose information and leads to solving for cos(theta) as +/-Something via arccos.

Areas of Agreement / Disagreement

Participants present multiple approaches and considerations, indicating that there is no consensus on a single method for solving the equation.

Contextual Notes

There are unresolved aspects regarding the implications of taking square roots and how they affect the solution set, particularly concerning the negative square root.

huskerfan5788
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This may seem really simple, but I just can't figure out how to do it.

Say you have an equation 0.651 = cos² (theta)

How would you solve for theta in degrees? I know that for cos (theta) you take the arccos, but what do you do when it is squared?

Thank you!
 
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I don't know. Maybe take square roots of both sides first?
 
And after you take the square root of both sides, consider taking the arc cosine (also called inverse cosine) of both sides.
 
Be warned that taking the square root is not enough. You'll also need to take the negative square root if you don't want to lose information...
 
If you just treat it like a quadratic I don't think you will lose any information.
0.651 = cos²
cos² - 0.651 = 0
cos² - 0cos - 0.651 = 0

Then you can solve for cos(theta) = +/-Something via arccos. I guess that's really the same as what was mentioned above though.
 

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