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

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

Ответ:

mandilynn22

01.01.2022

Mathematics

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

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

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Ответ:

queen3574

12.10.2021

Mathematics

Hello,

let's be a and b the sides of the rectangle.

1 area is 1600 =a*b
2. perimeter is 2(a+b)=160 ==> b=80-a

so,
1600=a*b=a*(80-a)==> 80a-a²=1600
==> a²-80a+1600=0
==> (a-40)²=0
==> a=40 or a=-40 (to exclude since < 0)
==> b=1600/40=40
the rectangle is a square of 40m of side.

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

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