Solve each equation for o is less than and/or equal to theta is less than and/or equal to 360
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sin^2x = 1 = cos^2x
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Work:
cos^2x - cos^2x = 0
0 = 0
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Textbook Answers:
90 and 270
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Btw, how would you isolate for cos^2x = 0? Would it be...
x = cos^-1 square root of _____ ?
Should this be...
sin^2x - 1 = cos^2x ??
Your equation has two equal signs.
Yeah it should be, sorry for the typo
Hmm... that's tricky. I solved it one way (similar to your method), and it didn't work. Anyway, this works...
(1) Subtract the cos^2(x) from both sides.
(2) Substitute "1 - sin^2(x)" in for cos^2(x). That comes from the #1 Identity: sin^2(x) + cos^2(x) = 1.
(3) Simplify and factor.
You should get the right answer that way. Let me know if you run into any problems.
To solve the equation cos^2x = 0, we can follow these steps:
1. Start with the equation cos^2x = 0.
2. Subtract cos^2x from both sides to obtain 0 - cos^2x = 0 - 0.
3. Simplify the equation to - cos^2x = 0.
4. Multiply both sides by -1: (-1)(- cos^2x) = 0 * -1.
5. This gives us cos^2x = 0.
Now, to isolate for x, we need to find the inverse cosine (also called arccosine) of both sides. The inverse cosine will give us the angle whose cosine is equal to 0.
To represent the inverse cosine function, we use cos^-1. Therefore, we have:
cos^-1(cos^2x) = cos^-1(0).
The inverse cosine and cosine will cancel out, leaving us with:
x = cos^-1(0).
Now, to evaluate cos^-1(0), we need to find the angle whose cosine is equal to 0. In other words, we need to find the angle for which the cosine function returns 0.
The answer to cos^-1(0) is the angle at which the x-coordinate of a point on the unit circle is 0. This occurs at two angles: 90 degrees and 270 degrees.
Therefore, x = 90 and x = 270.
So the solutions to the equation cos^2x = 0, within the given range of o is less than and/or equal to theta is less than and/or equal to 360, are 90 and 270.