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# If sin θ = √3 / 2 and tan θ < 0, what is the value of cos θ?

We will use the concepts of trigonometry to find the value of cos θ.

## Answer: If sin θ = √3 / 2 and tan θ < 0, the value of cos θ = -1 / 2.

Let us see how we will use the concept of trigonometry to find the value of cos θ.

**Explanation:**

It is given that sin θ = √3 / 2 and tan θ < 0.

Hence, we are talking about 2nd quadrant that is π / 2 < θ < π.

In the second quadrant, if sin θ = √3 / 2 then θ = 2π / 3 .

Therefore, cos (2π / 3) = - sin(π / 6) = -1 / 2 (Because cos is negative in 2nd quadrant)

### Therefore, cos θ = -1 / 2.

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