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Rzqust [24]
3 years ago
5

Given sin theta = 1/3 and 0 theta pi/2 find tan 2 theta

Mathematics
2 answers:
Kazeer [188]3 years ago
5 0

Answer:

\tan2\theta=\pm\dfrac{4\sqrt{2}}{7}

Step-by-step explanation:

Given: \sin\theta = \dfrac{1}{3}

0\leq \theta \leq \dfrac{\pi}{2}

Theta lie in first quadrant.

Multiply both sides by 2

0\leq 2\theta \leq \pi

2theta lie in I and II quadrant.

\tan2\theta is positive in I and negative in II quadrant.

\sin\theta=\dfrac{1}{3}

\cos\theta=\dfrac{2\sqrt{2}}{3}

\sin2\theta=2\sin\theta\cos\theta

\sin2\theta=2\cdot \dfrac{1}{3}\cdot \dfrac{2\sqrt{2}}{3}=\dfrac{4\sqrt{2}}{9}

\cos2\theta=\pm \sqrt{1-\sin^22\theta}=\pm\dfrac{7}{9}

\tan2\theta=\dfrac{\sin2\theta}{\cos2\theta}

\tan2\theta=\pm\dfrac{4\sqrt{2}}{7}

Hence, The value of \tan2\theta=\pm\dfrac{4\sqrt{2}}{7}

mrs_skeptik [129]3 years ago
3 0

Answer:

c on edge

Step-by-step explanation:

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