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Pythagorean Identities

Trigonometric identities bring new life to the Pythagorean theorem by re-envisioning the legs of a right triangle as sine and cosine. See more

Warmup

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

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

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

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?

Which of these is equivalent to \( x \)?

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

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