Transformations
Even/Odd & Co-functions
Solve or Evaluate - No Calculator!
100
Express \[\cos \left( {2x} \right)\] using only \[\sin \left( x \right)\].
\[1 - 2{\sin ^2}x\]
100
Rewrite the expression, filling in the blank: \[\_\_\_\_\_\left( {\frac{\pi }{3}} \right) = \sec \left( {\frac{\pi }{6}} \right)\]
\[\csc \left( {\frac{\pi }{3}} \right) = \sec \left( {\frac{\pi }{6}} \right)\]
100
Given that \[\tan x = - \frac{4}{3}\], for \[{90^ \circ } < x < {180^ \circ }\], find \[\sin (2x)\]
\[ - \frac{{24}}{{25}}\]
200
Express \[\sin \left( {6x} \right)\cos \left( {6x} \right)\] using only the sine function.
\[\frac{1}{2}\sin \left( {12x} \right)\]
200
Evaluate: \[Arc\cot \left( {\tan {{31}^ \circ }} \right)\]
\[{59^ \circ }\]
200
Given that \[\cos x = \frac{5}{{13}}\]for \[{270^ \circ } < x < {360^ \circ }\], find \[\sin \left( {\frac{1}{2}x} \right)\]. Express your answer in simplified radical form.
\[\frac{{2\sqrt {13} }}{{13}}\]
300
Transform \[\sin (4x)\tan (2x)\] into an expression that utilizes only \[\sin (x)\] and \[\cos (x)\] and does not contain a denominator.
\[8{\sin ^2}(x){\cos ^2}(x)\]
300
Rewrite the expression, filling in the blank: \[\sin ( - {80^ \circ }) = \_\_\_\_\_\_\_({10^ \circ })\]
\[\sin ( - {80^ \circ }) = - \cos ({10^ \circ })\]
300
Solve \[\sin (\theta + {40^ \circ }) = \frac{{\sqrt 2 }}{2}\] for \[x \in \{ {\rm{real numbers of degrees\} }}\]
\[{5^ \circ } + 360{n^ \circ }\]or\[{95^ \circ } + 360{n^ \circ }\]
400
Transform \[\cos (3x)\]in terms of \[\cos (x)\]alone.
\[4{\cos ^3}(x) - 3\cos (x)\]
400
Evaluate:\[Arc\cos \left[ {\sin \left( { - \frac{{3\pi }}{2}} \right)} \right]\]
0
400
Solve \[{\cos ^2}x - {\sin ^2}x = \frac{{\sqrt 3 }}{2}\] for\[x \in \left( {0,\frac{\pi }{2}} \right)\]
\[\frac{\pi }{{12}}\]
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