SOLUTION: 2 cos squared (75degrees)-1

Question 376518: 2 cos squared (75degrees)-1

Answer by jsmallt9(3759) (Show Source): You can put this solution on YOUR website!

There are three variations to the formula for cos(2x):

Your expression fits the middle variation with x = 75. Using the pattern for this formula, with 75 in the place of x, we get:
cos(2*75)
which simplifies to
cos(150)
The reference angle for 150, since it is in the second quadrant, is 180 - 150 or 30. This is one of the special angles whose sin's and cos's you are supposed to learn. cos(30) = And since 150 is in the second quadrant and cos is negative in the second quadrant...
cos(150) =

Note: If you simply use your calculator on the original expression, you will end up with a decimal. It would be difficult to recognize this decimal as . The decimal is an approximate answer. The square root answer is 100% exactly correct. The moral of the story, if you can use special angles on a problem, do so. You will end up with exact answers instead of decimal approximations. This is why we used the cos(2x) formula. It turned and expression with a non-special angle, 75, into an expression involving a special angle, 150.
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