Question 720143: please help me solve the following trigonometric equation using Pythagorean identity formula:
1-sin^2theta=0.5
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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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