Pythagorean Identities

Pythagorean Identities Warmup

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

\sin^2(\theta) = 1 - \cos^2(\theta)

\sin^2(\theta) - \cos^2(\theta) = 1

\sin^2(\theta) = \cos^2(\theta) - 1

\cos^2(\theta) - \sin^2(\theta) = 1

by Brilliant Staff

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

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

True False

by Brilliant Staff

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

\sin^2(\theta)

\tan^2(\theta)

\cos^2(\theta)

\sec^2(\theta)

by Brilliant Staff

Which of these is equivalent to $x$ ?

\cos(\theta)

\sec(\theta)

\csc(\theta)

\sin(\theta)

by Brilliant Staff

If $\sin^2(\theta) = \frac{9}{25}$ , what is $\cos^2(\theta) ?$

\frac{24}{25}

\frac{16}{25}

\frac{1}{5}

\frac{4}{5}

by Brilliant Staff

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