Flashcards
Trigonometric Identities
Cards in this deck (44)
- 1Trigonometric IdentitiesTrigonometric
Identities - 2\[\sin \theta = \] (definition)\[ \frac {\textrm{OPPOSITE}}{\textrm{HYPOTENUSE}} \]
- 3\[ \cos \theta = \] (definition)\[ \frac {\textrm{ADJACENT}}{\textrm{HYPOTENUSE}} \]
- 4\[ \tan \theta = \] (definition)\[ \frac {\textrm{OPPOSITE}}{\textrm{ADJACENT}} \]
- 5\[ \sec \theta = \]\[ \frac {1}{\cos\theta} \]
- 6\[ \csc \theta = \]\[ \frac {1}{\sin\theta} \]
- 7\[ \cot \theta = \]\[ \frac {1}{\tan\theta} \]
- 8\[ \tan \theta = \] (quotient)\[ \frac {\sin\theta}{\cos\theta} \]
- 9\[ \cot \theta = \] (quotient)\[ \frac {\cos\theta}{\sin\theta} \]
- 10\[ \cos^2\theta + \sin^2\theta = \]1
- 11\[ \cos^2\theta = \]\[ 1 - \sin^2\theta \]
- 12\[ \sin^2\theta = \]\[ 1 - \cos^2\theta \]
- 13\[ 1 + \tan^2 \theta = \]\[ \sec^2 \theta \]
- 14\[ \sec^2 \theta \]\[ 1 + \tan^2 \theta = \]
- 15\[\tan^2 \theta = \]\[\sec^2 \theta - 1 \]
- 16\[ 1 + \cot^2 \theta = \]\[ \csc^2 \theta \]
- 17\[ \csc^2 \theta \]\[ 1 + \cot^2 \theta = \]
- 18\[\cot^2 \theta = \]\[ \csc^2 \theta - 1 \]
- 19\[ \cos (\alpha + \beta) \]\[ \cos\alpha \cos\beta - \sin\alpha\sin\beta \]
- 20\[ \cos (\alpha - \beta) \]\[ \cos\alpha \cos\beta + \sin\alpha\sin\beta \]
- 21\[ \sin (\alpha + \beta) \]\[ \sin\alpha \cos\beta + \cos\alpha\sin\beta \]
- 22\[ \sin (\alpha - \beta) \]\[ \sin\alpha \cos\beta - \cos\alpha\sin\beta \]
- 23\[\sin 2\theta =\]\[2 \sin\theta \cos\theta\]
- 24\[\cos 2\theta =\]\[\cos^2 \theta - \sin^2 \theta\]
- 25\[\cos 2\theta =\]\[2 \cos^2 \theta -1\]
- 26\[\cos 2\theta =\]\[ 1 - 2\sin^2 \theta\]
- 27\[ \sin\left(\frac{\pi}{2}-\theta\right)=\]\[\cos\theta\]
- 28\[ \cos\left(\frac{\pi}{2}-\theta\right)=\]\[\sin\theta\]
- 29\[ \tan\left(\frac{\pi}{2}-\theta\right)=\]\[\cot\theta\]
- 30\[ \cot\left(\frac{\pi}{2}-\theta\right)=\]\[\tan\theta\]
- 31\[ \sec\left(\frac{\pi}{2}-\theta\right)=\]\[\csc\theta\]
- 32\[ \csc\left(\frac{\pi}{2}-\theta\right)=\]\[\sec\theta\]
- 33\[\sin(-\theta)=\]\[-\sin\theta\]
- 34\[\cos(-\theta)=\]\[\cos\theta\]
- 35\(\sin\theta\): odd or even?odd
- 36\(\cos\theta\): odd or even?even
- 37\[\tan(2\theta) = \]\[\frac{2\tan\theta}{1-\tan^2\theta}\]
- 38\[\cos^2\theta =\]\[ \frac{1+\cos 2 \theta}{2}\]
- 39\[\sin^2\theta = \]\[\frac{1-\cos 2 \theta}{2}\]
- 40\[\tan^2\theta = \]\[\frac{1-\cos 2 \theta}{1+\cos 2 \theta}\]
- 41\begin{equation*} \cos\left( \frac{\theta}{2} \right) = \end{equation*}\begin{equation*}
\pm \sqrt{\frac{1+\cos \theta}{2}}
\end{equation*} - 42\begin{equation*} \sin\left( \frac{\theta}{2} \right) = \end{equation*}\begin{equation*}
\pm \sqrt{\frac{1-\cos \theta}{2}}
\end{equation*} - 43\begin{equation*} \tan\left( \frac{\theta}{2} \right) = \end{equation*}\begin{equation*}
\pm \sqrt{\frac{1-\cos \theta}{1+\cos \theta}} = \frac{1-\cos \theta}{\sin \theta} = \frac{\sin \theta}{1+\cos \theta}
\end{equation*} - 44\[\tan(\alpha \pm \beta)=\]\[ \frac{\tan(\alpha)\pm \tan(\beta)}{1 \mp \tan(\alpha)\tan(\beta)}\]
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- High School Diploma Math (Precalculus) Flashcards on Trigonometric Identities, created by Bill Andersen on 02/08/2015.
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- Bill Andersen
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