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# If sin θ = -1 / 2 and π < θ < 3π / 2 , what are the values of cos θ and tan θ?

We will use the concepts of trigonometry to find the values of cos θ and tan θ.

## Answer: If sin θ = -1 / 2 and π < θ < 3π / 2, the values of cos θ and tan θ are cos θ = - √3 / 2 and tan θ = 1 / √3 respectively.

Let us see how we will use the concepts of trigonometry to find the values of cos θ and tan θ.

**Explanation:**

We have been given as sin θ = -1 / 2 . Using this we will calculate the value of θ .

Since, sin θ = -1 / 2

θ = - π / 6 or 7π / 6 [Using trigonometric table of standard angle values]

But the range of θ is given as π < θ < 3π / 2

Therefore, we will consider θ = 7π / 6

Now, cos ( 7π / 6 ) = cos ( π + π / 6 ) = - cos ( π / 6 ) = - √3 / 2 .

Similarly, tan ( 7π / 6 ) = tan ( π + π / 6 ) = tan ( π / 6 ) = 1 / √3

### Hence , cos θ = - √3 / 2 and tan θ = 1 / √3^{ }.

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