7.6+OFSA

OFSA for Solving Equations 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 \[Solve\;for\;3tan^2x-sec^2x-5=0\;over\;(-\infty ,\infty )\] math
 * Question 1**

math A.\;\;\;\;\[x=\frac{\pi }{6}+\pi n, \forall n\epsilon \mathbb{Z}\;or\;x=\frac{7\pi}{6}+\pi n, \forall n\epsilon \mathbb{Z}\] math

math B.\;\;\;\;x=\frac{\pi }{3}+\pi n, \forall n\epsilon \mathbb{Z} math

math C.\;\;\;\;x=\frac{\pi }{3}+\pi n, \forall n\epsilon \mathbb{Z}\;or\;x=\frac{2\pi }{3}+\pi n, \forall n\epsilon \mathbb{Z} math

math D.\;\;\;\;x=\frac{7\pi}{6}+\pi n, \forall n\epsilon \mathbb{Z} math Click here for solution.

math Solve\;for\;tan^2x+2tanx=3\;over\;[0,2\pi ] math math \[A.\;\;\;\;x=\frac{\pi}{4},\frac{5\pi}{4},\pi+Tan^{-1}(-3),2\pi+Tan^{-1}(-3)\] math
 * Question 2**

math \[B.\;\;\;\;x=\frac{\pi}{4},\frac{5\pi}{4},\pi-Tan^{-1}(-3),2\pi-Tan^{-1}(-3)\] math

math \[C.\;\;\;\;x=\frac{\pi}{4},\pi+Tan^{-1}(-3),2\pi+Tan^{-1}(-3)\\\] math

math \[D.\;\;\;\;x=\frac{\pi}{4},\frac{5\pi}{4},Tan^{-1}(-3)+\pi,Tan^{-1}(-3)+2\pi\] math

Click here for solution.

math \[Solve\;for\;6sin(\frac{1}{2}x)=3\;over\;[0,2\pi)\] math
 * Question 3**

math \[A.\;\;\;\;x\;\epsilon\;\frac{\pi}{6},\frac{5\pi}{6}\;over\;[0,2\pi)\] math

math \[B.\;\;\;\;x\;\epsilon\;\frac{\pi}{3},\frac{5\pi}{3}\;over\;[0,2\pi)\] math

math \[C.\;\;\;\;x\;\epsilon\;\frac{\pi}{3},\frac{5\pi}{3}\;over\;[0,2\pi)\] math

math \[D.\;\;\;\;x\;\epsilon\;\frac{\pi}{6},\frac{5\pi}{6},\frac{13\pi}{6},\frac{17\pi}{6}\;over\;[0,2\pi)\] math Click here for solution.

math {\text{Solve for X: }} 2\sin^2 x+ 3\cos x -3= 0 {\text{ over the interval } [0,2\Pi). \\
 * Question 4**

\begin{array}{*{20}{l}} &{0, 2\Pi , \frac{\Pi}{3}}&{} \\

&{0, 2\Pi , \frac{\Pi}{3} , \frac {5\Pi}{3}}&{} \\

&{0, \frac{\Pi}{3} ,\frac{5\Pi}{3}}&{} \\

&{0, 2\Pi }&{} \\ \end{array} math Click here for solution.

math 17\sin ^2x-3\cos ^2x=2 math
 * Question 5**
 * Solve for X:**

math A. \left ( \frac{\pi }{6},\frac{5\pi }{6} \right ) math

math B. \left (\frac{\pi }{6} ,\frac{5\pi }{6}, \frac{7\pi }{6},\frac{11\pi }{6} \right ) math

math C. \pm \frac{1}{2} math

D. No solution

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math \text{Solve for} {\theta} : math math (tan\theta)(sin\theta)-(cot\theta)(sin\theta)+(tan\theta)-(cot\theta)=0\;over\; [-\pi,\pi] math
 * Question 6**

math \text{A.}\theta = -\frac{\pi}{2} math math \text{B.} \theta = (-\frac{3\pi}{4}, -\frac{\pi}{4}, \frac{\pi}{4}, \frac{3\pi}{4}) math math \text{C.} \theta = (-\frac{3\pi}{4}, -\frac{\pi}{2} -\frac{\pi}{4}, \frac{\pi}{4}, \frac{3\pi}{4}) math math \text{D.} \theta = (-\frac{3\pi}{4}, \frac{\pi}{4}) math Click here for solution.

math \text{Solve for} {\theta} : math math sin\theta cos2\theta -cos\theta sin2\theta +3csc\theta =2 {\text{ over the interval } [0,4\pi). \\ math
 * Question 7**

math \text{A.}\theta = \frac{\pi}{2} math math \text{B.} \theta = Sin^{-1} (3) math math \text{C.} \theta = (\frac{\pi}{2}, \frac{5\pi}{2}) math math \text{D.} \theta = \frac{5\pi}{2} math Click here for solution.

Solve: math \sin \left ( 105 \right )=? math
 * Question 8**

math A. \left ( \frac{\sqrt{2}}{4}\right )+\left ( \frac{\sqrt{6}}{4} \right ) math

math B. \left ( \frac{\sqrt{2}}{4}\right )-\left ( \frac{\sqrt{6}}{4} \right ) math

math C. \left ( \frac{1}{2}\right )+\left ( \frac{\sqrt{3}}{4} \right ) math

D. Not enough information given in order to solve Click here for solution.

How many solutions are there going to be for x? math 4\sin ^2\left ( x \right )+1=4\sin \left ( x \right ), over:\left [ -\pi ,2\pi \right ] math
 * Question 9**

A. 2 B. 4 C. 6 D. Infinite Number of Solutions Click here for solution.

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 * Question 10**

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 * Question 11**

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 * Question 12**

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 * Question 13**

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 * Question 14**

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 * Question 15**

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 * Question 16**

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 * Question 17**

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 * Question 18**

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 * Question 19**

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 * Question 20**

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 * Question 22**

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 * Question 23**

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 * Question 24**