if sin a=0.5 then find the value of cos3a
To find the value of cos 3a given sin a = 0.5, we need to use trigonometric identities and algebraic manipulation.
First, we can use the Pythagorean identity to find the value of cos a:
sin^2 a + cos^2 a = 1
0.5^2 + cos^2 a = 1
0.25 + cos^2 a = 1
cos^2 a = 1 - 0.25 = 0.75
cos a = sqrt(0.75) ≈ 0.866
Next, we can apply the triple-angle identity for cosine:
cos 3a = 4 * cos^3 a - 3 * cos a
Substituting the value of cos a we found earlier:
cos 3a = 4 * (0.866)^3 - 3 * 0.866
Calculating the value:
cos 3a ≈ 4 * 0.6586 - 2.598
cos 3a ≈ 2.6344 - 2.598
cos 3a ≈ 0.0364
Therefore, the value of cos 3a is approximately 0.0364.
sin(a)=0.5
use sin²(a)+cos²(a)=1
0.5²+cos²(a) = 1
cos²(a)=3/4
cos(a)=sqrt(3)/2
cos³(a)=(3/8)sqrt(3)