Geometry

Pythagorean Identities

Pythagorean Identities Warmup

         

Given sin2(θ)+cos2(θ)=1 \sin^2(\theta) + \cos^2(\theta) = 1 , which of the following is true?

True or False: sin2(θ)cos2(θ)+1=2sin2(θ) \sin^2(\theta) - \cos^2(\theta) + 1 = 2\sin^2(\theta) .

(Hint: Use the identity sin2(θ)+cos2(θ)=1 \sin^2(\theta) + \cos^2(\theta) = 1 .)

Which is these is equivalent to cos2(θ)sec2(θ)cos2(θ), \cos^2(\theta)\sec^2(\theta) - \cos^2(\theta), over values of θ\theta for which the given expression is defined?

Which of these is equivalent to x x ?

If sin2(θ)=925 \sin^2(\theta) = \frac{9}{25} , what is cos2(θ)? \cos^2(\theta) ?

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