Let's Review
Trigonometric identities are equations that involve trigonometric functions and are true for every value of the variables involved. The trigonometric identities you have learned in previous lessons are shown below. Click each tab to see the identities.
tangent quotient
identity
\( \tan\theta = \frac{\sin\theta}{\cos\theta} \)
cotangent quotient
identity
\( \cot\theta = \frac{\cos\theta}{\sin\theta} \)
cosecant reciprocal
identity
\( \csc\theta = \frac{1}{\sin\theta} \)
secant reciprocal
identity
\( \sec\theta = \frac{1}{\cos\theta} \)
cotangent reciprocal
identity
\( \cot\theta = \frac{1}{\tan\theta} \)
sine and cosine
Pythagorean identity
\( \sin^{2}\theta + \cos^{2}\theta = 1 \)
tangent and secant
Pythagorean identity
\( \tan^{2}\theta + 1 = \sec^{2}\theta \)
cotangent and cosecant
Pythagorean identity
\( \cot^{2}\theta + 1 = \csc^{2}\theta \)
tangent even-odd identity
\( \sin{( - \theta)} = - \sin\theta \), sine is odd
tangent even-odd identity
\( \cos{( - \theta)} = \cos\theta \), sine is even
tangent even-odd identity
\( \tan{( - \theta)} = - \tan\theta \), tangent is odd
sine cofunction identity
\( \sin\left( \frac{\pi}{2} - \theta \right) = \sin{(90{^\circ}} - \theta) = \cos\theta \)
cosine cofunction identity
\( \cos\left( \frac{\pi}{2} - \theta \right) = \cos{(90{^\circ}} - \theta) = \sin\theta \)
tangent cofunction identity
\( \tan\left( \frac{\pi}{2} - \theta \right) = \tan{(90{^\circ}} - \theta) = \cot\theta \)
cotangent cofunction identity
\( \cot\left( \frac{\pi}{2} - \theta \right) = \cot{(90{^\circ}} - \theta) = \tan\theta \)
secant cofunction identity
\( \sec\left( \frac{\pi}{2} - \theta \right) = \sec{(90{^\circ}} - \theta) = \csc\theta \)
cosecant cofunction identity
\( \csc\left( \frac{\pi}{2} - \theta \right) = \csc{(90{^\circ}} - \theta) = \sec\theta \)
Think You Got It?
Look over this list of identities you have learned so far. Match each term on the left with the correct description on the right.
