Answer:
Theta = 346.44 degrees
Explanation:
If cos(theta) = -0.9659, we can use the inverse cosine function (cos^-1) to find theta. Here's how we can solve it:
cos(theta) = -0.9659
cos^-1(cos(theta)) = cos^-1(-0.9659) [applying cos^-1 to both sides]
theta = 2π - cos^-1(0.9659) [using the fact that cos(theta) is negative in the third quadrant]
Using a calculator, we can evaluate cos^-1(0.9659) as 15.56 degrees (rounded to two decimal places). Therefore:
theta = 2π - 15.56 degrees
theta = 346.44 degrees
So, theta is 346.44 degree.