To find this value we can use the fact, that we know cos30 (cos30 = √3 2) cos30 = cos2 ⋅ 15 = cos215 −sin215 On the other hand sin215 +cos215 = 1, so we can make a system of equations: To simplify the notation I will use s for sin15 and c for cos15 {c2 + s2 = 1 c2 − s2 = √3 2 If we add both sides of the equations we get: 2c2 = 2 + √3 2

Jul 19, 2015 · I found: cos (15°)=0.9659 We use the half angle formula: cos^2 (x)=1/2 [1+cos (2x)] with x=15° and so 2x=30° so: cos^2 (15°)=1/2 [1+cos (30°)] we know that cos (30°)=sqrt (3)/2 so: cos^2 (15°)=1/2 [1+sqrt (3)/2] cos^2 (15°)= (2+sqrt (3))/4 square root both sides: cos (15°)=+-sqrt ( (2+sqrt (3))/4)=+-0.9659 We choose the positive value.

Oct 10, 2015 · cos(15o) is in Quadrant I which means the answer must be a positive value. Use the half-angle formula to solve it.

Aug 4, 2015 · Find cos 105 Ans: (2 - sqrt3)/2 cos 105 = cos (15 + 90) = - sin 15 cos 30 = sqrt3/2 = 1 - 2sin^2 (15) 2sin^2 15 = (2 - sqrt3)/2 sin^2 15 = (2 - sqrt3)/4 --> sin 15 = +- (2 - sqrt3)/2 Since the arc 15 is in Quadrant I, therefor, only the positive answer is accepted. cos 105 = - sin 15 = - (2 …

I consider cos(30°)=sqrt(3)/2 as a fundamental value so: The last expression can be calculated by hand.

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