<PRE><B>Question 720143</B>
i will use the letter T to represent theta.


the pythagorean identify is sin^2(T) + cos^2(T) = 1


subtract sin^2(T) from both sides of this equation to get:


cos^2(T) = 1 - sin^2(T)


your equation is 1 - sin^2(T) = .5


since 1 - sin^2(T) is equivalent to cos^2(T), replace 1 - sin^2(T) with cos^2(T) and you get:


cos^2(T) = .5


take the square root of both sides of this equation to get:


cos(T) = +/- sqrt(.5)


cos(T) can be + sqrt(.5) or - sqrt(.5)


if + sqrt(.5), then T is equal to 45 degrees.


if - sqrt(.5), then T is equal to 135 degrees.


to find the angle whose cosine is equal to sqrt(.5), you use the cos^-1 function of your calculator.


the key to solving this, however, is to recognize that:
1 - sin^2(T) 
is equivalent to cos^2(T) based on the pythagorean formula of:
sin^2(T) + cost^2(T) = 1.


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