Question

Найдите значение cos(a-60),если sin a=1/3 и 90

Answer 1

Cosa=-√(1-sina)=-√(1-1/9)=-√(8/9)=-2√2/3
cos(a-60)=cosa*cos60+sina*sin60=-2√2/3*1/2+1/3*√3/2=(-2√2+√3)/6

Answer 2

Since sin(a) = 1/3 and a is in the second quadrant (90° < a < 180°), we can use the Pythagorean identity to find cos(a):

cos(a) = sqrt(1 - sin^2(a)) = sqrt(1 - (1/3)^2) = sqrt(8/9) = (2*sqrt(2))/3

Now we can use the difference identity for cosine:

cos(a - 60) = cos(a)cos(60) + sin(a)sin(60)

Since cos(60) = 1/2 and sin(60) = sqrt(3)/2, we can substitute in these values:

cos(a - 60) = (2sqrt(2))/3 * (1/2) + (1/3) * (sqrt(3)/2) = sqrt(2)/3 + (sqrt(3)/6) = (2sqrt(6) + 3*sqrt(2)) / 6

Therefore, cos(a-60) = (2sqrt(6) + 3sqrt(2)) / 6.