7.5+OFSA

OFSA for Verifying and Simplifying Using Trigonometric IDs This page contains peer generated questions that help you assess your understanding. Remember that questions may not represent the rigor of the questions you may be expected to complete on formal assessments. This page is simply an OFSA - opportunity for self assessment.

math {\text{Which one expression below is equivalent to: }}\sin \left( {x - \frac{\pi }{6}} \right) + \sin \left( {x + \frac{\pi }{6}} \right)?
 * Sample Question**

\begin{array}{*{20}{l}} &{\text{0}}&{} \\ &{ 1/2 }&{} \\ &{\cos x}&{} \\ &{ - \sqrt 3 \cos x}&{} \end{array} math

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math {\text{Find the exact value of: }} \cos(75^{\circ})
 * Question 1**

\begin{array}{*{20}{l}} &{\frac{-\sqrt 6-\sqrt2}{4} \\ &{\frac{\sqrt 6-\sqrt2}{4} \\

&{\frac{\sqrt 6+\sqrt2}{4} \\

&{\frac{-\sqrt 6+\sqrt2}{2} \\ \end{array} math Click here for solution.

math {\text{Which is equal to: }} 2\sin \frac{\Pi}{6} \cos \frac{\Pi}{6}
 * Question 2**

\begin{array}{*{20}{l}} &{\sqrt 3}&{} \\ &{\frac{1}{2}}&{} \\ &{\sin^{-1}\frac{\Pi}{12}}&{} \\ &{\frac{\sqrt3}{2}}&{} \end{array} math

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 * Question 3**

math {\text { Evaluate}} \;\; 4 \cos ^{2}(\frac{\pi}{6})-2 \\ \\ \begin{array}{*{20}{l}} {\text A.} \; \sqrt{3} \\ {\text B.} \; 1 \\ {\text C.} \; -\sqrt{3} \\ {\text D.} \; -1 \end{array} math Click here for solution.

math {\text{Simplify: }} \left ( \tan^{2}x+1 \right )\left ( cos^{2}(-x)-1 \right )-tan^{2}(-x)
 * Question 4**

\begin{array}{*{20}{l}} &{2\tan^{2}x}&{} \\ &{0}&{} \\ &{-2\tan^{2}x}&{} \\ &{-1+\tan^{2}x}&{} \end{array} math Click here for solution.

math {\text {Simplify: }} \; \frac{(\sin x\cos x)^{2}}{\sin x\cos x} \\ \\ {\text {A.} \sec x\csc x - 2} \\
 * Question 5**

{\text {B.} \sec x\csc x +2} \\

{\text {C.} \sec x\csc x - 1} \\

{\text {D.} \sec x\csc x + 1} \\ math Click here for solution.

math {\text {Evaluate:}} \; \frac{11\pi}{3} \\ {\text {A.}} \;\; -\sqrt{3} \\ {\text {B.}} \;\;\; \sqrt{3} \\ {\text {C.}} \;\; -\frac{\sqrt{3}}{3} \\ {\text {D.}} \;\;\; \frac{\sqrt{3}}{3} math Click here for solution.
 * Question 6**

math \[Evaluate: sin(45)cos(30)+cos(45)(sin30)\] math math \[A. sin(15)\] math math \[B. sin(75)\] math math \[C. sin(\frac{\sqrt{6}-\sqrt{2}}{4})\] math math \[D. sin(\frac{\sqrt{2}}{4})\] math Click here for solution.
 * Question 7**

math \[Evaluate: Tan(\frac{\sqrt{3}}{3})\] math math \[A. \frac{\Pi }{6}, \frac{7\Pi }{6}\] math math \[B. \frac{5\Pi }{6}, \frac{11\Pi }{6}\] math math \[C. \frac{7\Pi }{6}\] math math \[D. \frac{\Pi }{6}\] math Click here for solution.
 * Question 8**

math \[Evaluate: cos(-x)+sin(x)\] math math \[A. -1\] math math \[B. 1\] math math \[C. 0\] math D Not possible Click here for solution.
 * Question 9**

Solve: math (cos (5\pi/12))(cos (\pi/12)) + (sin (5\pi/12))(sin (\pi/12)) math
 * Question 10**

math \text{A. } \frac{1}{2} \\ math

math \text{B. } 0 \\ math

math \text{C.} \frac{\sqrt{3}}{2}} \\ math

math \text{D. } 1 \\ math

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math \textup{Evaluate:}\ \left (1-\cos x\right )\left ( \csc x+\cot x \right )\\ \textup{A.}\ \sin x \\ \textup{B.}\ \frac{1-\cos x }{\sin x}\\ \textup{C.}\ \frac{\cot^{2} x}{\sin x}\\ \textup{D.}\ \textup{Cannot be evaluated.} math Click here for solution.
 * Question 11**

math \textup{Simplify:}\ \frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}\\\\ \textup{A.}\ \frac{2\cos x}{\sin x\left (1+\cos x \right )} \\ \textup{B.}\ 2\sec x\\ \textup{C.}\ \sin x+1+\cos x\\ \textup{D.}\ 2\csc x \\ math Click here for solution.
 * Question 12**

math
 * Question 13**

\[y=x^{2}-x^{88}\]

math

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 * Question 14**

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 * Question 24**