Question

What is the exact value of cos(195°)?

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31-19-
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Answer 1

The exact value of cos(195°) is -√(2 + √3)/2, using reference angles and half-angle identities.

Step-by-step explanation:

The question asks for the exact value of cos(195°). To find the cosine of an angle greater than 180°, we can use reference angles and the unit circle. The reference angle for 195° is 195° - 180° = 15°. Cosine is negative in the third quadrant where 195° lies. The cosine of 15°, which can be derived using half-angle identities, is √(2 + √3)/2.

So, cos(195°) = -cos(15°) = -√(2 + √3)/2.

Answer 2

-
`\frac{\sqrt{2+√(3) } }{2}`

Step-by-step explanation:

using the half angle formula

cos(
`(x)/(2)` ) = ±
`\sqrt{(1+cosx)/(2) }`

cos195° = cos(180 + 15)° = - cos15°

then

cos15° = cos (
`(30)/(2)` ) =
`\sqrt{(1+cos30)/(2) }` =
`\sqrt{(1+(√(3) )/(2) )/(2) }` =
`\sqrt{(2+√(3) )/(4) }` =
`\frac{\sqrt{2+√(3) } }{2}`

then

cos195° = - cos15° = -
`\frac{\sqrt{2+√(3) } }{2}`