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Q. How do you find the exact value of cos(theta) if sin(theta)= - 2/3? Explain.​

Answer 1

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√(13/9)

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We know that

Sin² (theta) + Cos²(theta) = 1

So, filling the value of sin theta , we get

(-⅔)² + Cos²(theta) = 1

- 4/9 + Cos²(theta) = 1

Cos² (theta) = 1 + 4/9

Taking LCM

Cos² (theta) = (9 + 4)/9

Cos² (theta) = 13/9

So, finally Cos theta = √(13/9)

Answer 2

We know that

Sin² (theta) + Cos²(theta) = 1

So, filling the value of sin theta , we get

(-⅔)² + Cos²(theta) = 1

- 4/9 + Cos²(theta) = 1

Cos² (theta) = 1 + 4/9

Taking LCM

Cos² (theta) = (9 + 4)/9

Cos² (theta) = 13/9

So, finally Cos theta = √(13/9)