Find the exact values of the following:
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Find the exact values of the following:

[From: ] [author: ] [Date: 11-12-09] [Hit: ]
-1. Convert π/4 to degrees.2. Draw the angle. Should be on Quadrant I.3.......
If Θ = π/4,

what is 4 cos Θ?

in exact values? not approximate. How do I go about doing this without a calculator?

-
1. Convert π/4 to degrees.

(180/π) * (π/4) = 180/4 = 45°

--> 4 * cos(45°)

2. Draw the angle. Should be on Quadrant I.

3. Draw the triangle. So it is a 45°-45°-90° angle, meaning that the two legs are t and t. The hypotenuse is t√2.

4. t = 1; t = 1; t√2 = √2


so..

cos(45°) = 1/√2 * (√2/√2) --> (√2)/2

5. Don't forget the 4: 4 * (√2)/2 = 4√2/2 --> 4 reduces to 2 and 2 reduces to 1

FINAL ANSWER: 4cosθ = (√2)/2
1
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