Troubleshooting Trig Identities and Equations

[zizkio46]

Homework Statement

cos(squared)x = sinx-1/2

Homework Equations

cos(squared)x= 1-sin(squared)x

The Attempt at a Solution

I tried everything but my answer does not match my answers in calculator

 

[jhicks]

If $$cos^2(x) = sin(x)-0.5$$ and $$cos^2(x) = 1-sin^2(x)$$, then wouldn't you agree that $$sin(x)-0.5 = 1-sin^2(x)$$? That's a quadratic equation.

 

[Architeuthis Dux]

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It's important to remember that calculators can sometimes give rounded or approximate answers, so it's always best to double check your work by hand. In this case, it looks like you may have made a mistake in your algebraic manipulation. Remember that the identity for cos(squared)x is 1-sin(squared)x, not sinx-1/2. So, your equation should be cos(squared)x = 1-sin(squared)x. From there, you can use the Pythagorean identity (sin(squared)x + cos(squared)x = 1) to solve for sin(squared)x, and then take the square root to find sinx. Keep practicing and don't be afraid to ask for help if you get stuck!