Скачать или смотреть Find the exact value of the cosine of 165 degrees using addition properties

Find the exact value of the cosine of 165 degrees using addition properties
To find the exact value of cos(165°), we can use the **cosine addition formula**:

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

We can express 165° as the sum of two known angles:
165° = 180° - 15°

Now, use the cosine addition formula:

cos(165°) = cos(180° - 15°)

Using the cosine and sine values for 180° and 15°, we know:
cos(180°) = -1
sin(180°) = 0
cos(15°) = 2 - √3 (from earlier calculation)
sin(15°) = √10/10 (from earlier calculation)

Substitute these values into the formula:

cos(165°) = cos(180°)cos(15°) - sin(180°)sin(15°)
= (-1)(2 - √3) - (0)(√10/10)

Simplify the expression:

cos(165°) = -(2 - √3)
= -2 + √3

So, the exact value of cos(165°) is:

cos(165°) = -2 + √3