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

In summary, the conversation is about solving an equation involving a squared cosine function. The solution is to take the square root of both sides and then use the arccosine function to find the value of theta in degrees. It is important to take the negative square root as well in order to not lose any information. The process is similar to solving a quadratic equation.
  • #1
huskerfan5788
1
0
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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  • #2
I don't know. Maybe take square roots of both sides first?
 
  • #3
And after you take the square root of both sides, consider taking the arc cosine (also called inverse cosine) of both sides.
 
  • #4
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...
 
  • #5
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.
 

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

1. What are the basic trigonometric functions?

The basic trigonometric functions are sine, cosine, and tangent. These functions represent the ratios of the sides of a right triangle and are used to calculate angles and side lengths.

2. How do I convert degrees to radians?

To convert degrees to radians, simply multiply the number of degrees by π/180. This will give you the equivalent value in radians.

3. What is the unit circle and how is it used in trigonometry?

The unit circle is a circle with a radius of 1 unit. It is used in trigonometry to visualize the relationship between angles and the trigonometric functions. The coordinates of points on the unit circle correspond to the values of the trigonometric functions for that angle.

4. What is the difference between sine and cosine?

Sine and cosine are both trigonometric functions, but they have different definitions. Sine represents the ratio of the opposite side to the hypotenuse in a right triangle, while cosine represents the ratio of the adjacent side to the hypotenuse.

5. How do I find the inverse trigonometric functions?

The inverse trigonometric functions can be found using a calculator or by using the inverse trigonometric identities. For example, to find the inverse sine of a value, use the formula sin^-1(x) = arcsin(x).

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