Please evaluate cos 15 degrees
After doing several very similar type of questions like this with you, I hope you can handle this one.
Hint: cos15º = cos(45-30)º
To evaluate cos 15 degrees, you can use the trigonometric identity involving half-angle formulas.
The half-angle formula for cosine states that cos(x/2) = ±√((1 + cos(x))/2), where x is the angle in radians.
To apply this formula to cos 15 degrees, we need to convert 15 degrees to radians. The conversion factor is π/180, so 15 degrees in radians is (15 * π)/180 = π/12.
Now, substitute π/12 for x in the half-angle formula:
cos(π/12/2) = ±√((1 + cos(π/12))/2)
Next, evaluate cos(π/12) using either a calculator or a trigonometric table. The value of cos(π/12) is approximately 0.9659258262890683.
Now, substitute this value into the half-angle formula:
cos(π/12/2) = ±√((1 + 0.9659258262890683)/2)
Simplifying further, we get:
cos(15 degrees) = ±√(1.9659258262890683/2)
cos(15 degrees) ≈ ±√(0.9829629131445341)
The ± sign indicates that the cosine function has two possible values, positive and negative. Therefore, cos 15 degrees can be either approximately +0.991 or approximately -0.991.