solve the following system of equations algebraically (-2π, 2π)

y=cos^2 (x)

y=sin^2 (x) + 1/2

please show all work

Thanks

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- June 13th 2008, 05:30 PMmeli3000trig
solve the following system of equations algebraically (-2π, 2π)

y=cos^2 (x)

y=sin^2 (x) + 1/2

please show all work

Thanks - June 13th 2008, 05:34 PMsean.1986
Cos^2(x) = Sin^2(x) + 1/2

Cos^2(x) - Sin^2(x) = 1/2

Cos(2x) = 1/2

2x = Cos^-1(1/2)

x = (Cos^-1(1/2))/2 - June 13th 2008, 05:52 PMsean.1986
In fact, it's...

pi/6, 5pi/6, -pi/6, -5pi/6 - June 13th 2008, 08:06 PMSoroban
Hello, meli3000!

Quote:

Solve the following system of equations algebraically

. .

. .

Substitute into [1]: .

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- June 13th 2008, 08:12 PMsean.1986
Ah yeah forgot that because it's double you get 2 more answers. Oops!