Question

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Answer 1

Given:

The terminal point of
`\theta` is
`\left((1)/(2),(√(3))/(2)\right)`.

To find:

The value of
`\sin \theta`.

Solution:

If the terminal point of
`\theta` is
`(x,y)`, then

`\sin \theta = (y)/(√(x^2+y^2))`

The terminal point of
`\theta` is
`\left((1)/(2),(√(3))/(2)\right)`. So,

`\sin \theta = \frac{(√(3))/(2)}{\sqrt{\left((1)/(2)\right)^2+\left((√(3))/(2)\right)^2}}`

`\sin \theta = \frac{(√(3))/(2)}{\sqrt{(1)/(4)+(3)/(4)}}`

`\sin \theta = ((√(3))/(2))/(√(1))`

`\sin \theta = ((√(3))/(2))/(1)`

`\sin \theta =(√(3))/(2)`

Therefore, the correct option is B.