Question

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

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Answer 1

`\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`

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}`