Question

Cos(−θ)=√3/3, sinθ<0

What is the value of sin θ?

2√3/3
- √6/3
- 2√3/3
√6/3

Answer 1

Explanation:

Answer 2

`\sin\theta=-(√(6))/(3)`

Explanation:

The given trigonometric equation is
`\cos(-\theta)=(√(3) )/(3)`.

We can either use the Pythagorean identity or the right angle triangle to solve for
`\sin\theta`.

According to the Pythagorean identity,

`\cos^2\theta+\sin^2\theta=1`

Recall that, the cosine function is an even function, therefore

`\cos(-\theta)=\cos(\theta)`

`\Rightarrow \cos(\theta)=(√(3) )/(3)`.

We substitute this value in to the above Pythagorean identity to get;

`((√(3))/(3))^2+\sin^2\theta=1`

`\Rightarrow (3)/(9)+\sin^2\theta=1`

`\Rightarrow \sin^2\theta=1-(3)/(9)`

`\Rightarrow \sin^2\theta=(6)/(9)`

`\Rightarrow \sin\theta=\pm \sqrt{(6)/(9)}`

`\Rightarrow \sin\theta=\pm (√(6))/(3)`

But we were given that,

`\sin\theta\:<0\:`, so we choose the negative value.

`\Rightarrow \sin\theta=-(√(6))/(3)`

The correct answer is B