Question

What is the exact value of cosine (startfraction 11 pi over 12 endfraction)? negative startfraction startstartroot 2 + startroot 3 endroot endendroot over 2 endfraction negative startfraction startstartroot 2 minus startroot 3 endroot endendroot over 2 endfraction startfraction startstartroot 2 minus startroot 3 endroot endendroot over 2 endfraction startfraction startstartroot 2 + startroot 3 endroot endendroot over 2 endfraction

Answer 1

The exact value of the cosine of 11π / 12 will be given as negatice (1 + √3)/(2√2).

What is trigonometry?

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The trigonometric expression is given below.

⇒ cos (11π/12)

We know that 11π/12 is equal to 165 degrees. Then we have

cos 165° = cos (45° + 120°)

We know that

cos (A + B) = cos A cos B - sin A sin B

Then we have

cos (45° + 120°) = cos 45° cos 120° - sin 45° sin 120°

cos (45° + 120°) = 1/√2 x (- 1/2) - 1/√2 x √3/2

cos (45° + 120°) = - (1 + √3)/(2√2)

More about the trigonometry link is given below.

https://brainly.com/question/22698523

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