If Θ = π/4,
what is 4 cos Θ?
in exact values? not approximate. How do I go about doing this without a calculator?
what is 4 cos Θ?
in exact values? not approximate. How do I go about doing this without a calculator?
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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
(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