Trig Identities Jeopardy

Pythagorean Properties

100

Express \[1 - {\cos ^2}x\] in terms of one trig function.

\[{\sin ^2}x\]

200

Give a Pythagorean Trig Property that contains secant.

\[{\tan ^2}x+ 1 = {\sec ^2}x\]

300

Simplify: \[{\csc ^2}x - {\cot ^2}x\]

1

400

Simplify: \[{\tan ^2}x - {\sec ^2}x\]

-1

500

Express \[{\tan ^2}x - {\sec ^2}x + {\sin ^2}x\] using only one trigonometric function.

\[ - {\cos ^2}x\]

Co-functions

100

Express \[\sin \left( {\frac{\pi }{2} - x} \right)\] as the trig function of a single argument.

\[\cos x\]

200

Express \[\cot x\]using its co-function.

\[\tan \left( {\frac{\pi }{2} - x} \right)\]

300

\[Arc\cos \left[ {\sin \left( {{{34}^ \circ }} \right)} \right]\]

\[{56^ \circ }\]

400

\[Arc\cot \left[ {\tan \left( {\frac{\pi }{6}} \right)} \right]\]

\[\frac{\pi }{3}\]

500

\[Arc\sec \left[ {\csc \left( {{{17.9}^ \circ }} \right)} \right]\]

\[{72.1^ \circ }\]

Double Argument Properties

100

Express \[\cos (A - B)\] using only single argument(s) A and/or B.

\[\cos A\cos B + \sin A\sin B\]

200

Express \[\sin (A + B)\] using only single argument(s) A and/or B.

\[\sin A\cos B + \cos A\sin B\]

300

Express \[\tan (A - B)\] using only the tangent function of single argument(s) A and/or B.

\[\frac{{\tan A - \tan B}}{{1 + \tan A\tan B}}\]

400

Find the exact value of \[\sin ({75^ \circ })\]

\[\frac{{\sqrt 2 + \sqrt 6 }}{4}\]

500

Find the exact value of \[\cos \left( {{{105}^ \circ }^{}} \right)\]

\[ - \frac{{\sqrt 6 - \sqrt 2 }}{4}\]