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Trigonometry - Identities and double angle formulas

Authored by Karen Carcamo

Other

10th - 12th Grade

CCSS covered

Used 72+ times

Trigonometry - Identities and double angle formulas
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10 questions

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1.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Solve  cos⁡2x−cos⁡x=0\cos2x-\cos x=0   for  0≤x≤2π0\le x\le2\pi  .

 0, 2π3, 4π3, 2π0,\ \frac{2\pi}{3},\ \frac{4\pi}{3},\ 2\pi  

 5π6, 7π6\frac{5\pi}{6},\ \frac{7\pi}{6}  

 π3, 5π3\frac{\pi}{3},\ \frac{5\pi}{3}  

 π4,3π4, 5π4\frac{\pi}{4},\frac{3\pi}{4},\ \frac{5\pi}{4}  

Tags

CCSS.HSF.TF.B.7

2.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Given that  sin⁡θ=−56, 3π2≤θ≤2π\sin\theta=-\frac{5}{6},\ \frac{3\pi}{2}\le\theta\le2\pi  , find  cos⁡ 2θ\cos\ 2\theta  .

 1012\frac{10}{12}  

 −51118-\frac{5\sqrt{11}}{18}  

 −718-\frac{7}{18}  

 −1012-\frac{10}{12}  

3.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

If  cos⁡β=25\cos\beta=\frac{2}{5}  where  270°≤β≤360°270\degree\le\beta\le360\degree  , find  sin⁡2β\sin2\beta   .

 −42125-\frac{4\sqrt{21}}{25}  

 42125\frac{4\sqrt{21}}{25}  

 435\frac{4\sqrt{3}}{5}  

 −435-\frac{4\sqrt{3}}{5}  

Tags

CCSS.HSF.TF.C.9

4.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Simplify  sin⁡(π−θ)−sin⁡(−θ)cos⁡ (−θ)\frac{\sin\left(\pi-\theta\right)-\sin\left(-\theta\right)}{\cos\ \left(-\theta\right)}  

 00  

 2tan⁡θ2\tan\theta  

 1cos⁡ θ\frac{1}{\cos\ \theta}  

 tan⁡θ\tan\theta  

5.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Solve for  0≤x≤2π0\le x\le2\pi  ,  sin⁡x=sin⁡ 2x\sin x=\sin\ 2x  .

0

 0, π3, π, 5π3, 2π0,\ \frac{\pi}{3},\ \pi,\ \frac{5\pi}{3},\ 2\pi  

 0, 2π0,\ 2\pi  

 0, π6,11π6, 2π0,\ \frac{\pi}{6},\frac{11\pi}{6},\ 2\pi  

6.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Solve  sin⁡θcos⁡θ=14\sin\theta\cos\theta=\frac{1}{4}  for  −π≤θ≤π-\pi\le\theta\le\pi  .

 ±π12,±5π12\pm\frac{\pi}{12},\pm\frac{5\pi}{12}  

 −7π6,−11π6,π6, 5π6-\frac{7\pi}{6},-\frac{11\pi}{6},\frac{\pi}{6},\ \frac{5\pi}{6}  

 ±π6,±5π6\pm\frac{\pi}{6},\pm\frac{5\pi}{6}  

 −11π12,−7π12,π12,5π12-\frac{11\pi}{12},-\frac{7\pi}{12},\frac{\pi}{12},\frac{5\pi}{12}  

7.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

If  sin⁡θ=45\sin\theta=\frac{4}{5}  and  cos⁡θ=35\cos\theta=\frac{3}{5}  find  tan⁡2θ\tan2\theta  .

 −724-\frac{7}{24}  

 247\frac{24}{7}  

 724\frac{7}{24}  

 −247-\frac{24}{7}  

Tags

CCSS.HSF.TF.C.9

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