If angle x lies in quadrant 3 and cos(x)= -0.6
Find cos(3pi/2-x)
To find cos(3π/2 - x), we can use the identity: cos(a - b) = cos(a)cos(b) + sin(a)sin(b).
In this case, let's set a = 3π/2 and b = x.
cos(3π/2 - x) = cos(3π/2)cos(x) + sin(3π/2)sin(x)
First, let's determine the values of sin(3π/2) and cos(3π/2).
In quadrant 3, the cosine is negative, and the sine is positive. Therefore, cos(3π/2) = 0 and sin(3π/2) = -1.
Now, let's substitute these values into the equation:
cos(3π/2 - x) = 0 * cos(x) + (-1) * sin(x)
= -sin(x)
Since we know that cos(x) = -0.6, we can rewrite the expression:
cos(3π/2 - x) = -(-0.6)
= 0.6
Therefore, cos(3π/2 - x) = 0.6.