Question

Sin tita= 0.6892.find the value Of tita correct to two decimal places​

Answer 1

Answer:

$\theta \approx 6.28n + 2.38, \quad n \in \mathbb{Z}$

or

$\theta \approx 6.28n + 0.76, \quad n \in \mathbb{Z}$

Considering $\theta \in (0, 2\pi]$

$\theta \approx 2.38$

or

$\theta \approx 0.76$

Step-by-step explanation:

$\sin(\theta)=0.6892$

We have:

$\sin (x)=a \Longrightarrow x=\arcsin (a)+2\pi n \text{ or } x=\pi -\arcsin (a)+2\pi n \text{ as } n\in \mathbb{Z}$

Therefore,

$\theta= \arcsin (0.6892)+2\pi n, \quad n \in \mathbb{Z}$

or

$\theta = \pi -\arcsin (0.6892)+2\pi n, \quad n\in \mathbb{Z}$

---------------------------------

$\theta \approx 6.28n + 2.38, \quad n \in \mathbb{Z}$

or

$\theta \approx 6.28n + 0.76, \quad n \in \mathbb{Z}$