Solve for theta in the equation cos(2theta-30degrees)=-0.7660 for -180<theta>180
To solve for theta, we can manipulate the equation and use the inverse cosine function, also known as arccosine.
Given: cos(2θ - 30°) = -0.7660
Rearranging the equation:
2θ - 30° = arccos(-0.7660)
Now, use the inverse cosine function on both sides of the equation:
θ = (arccos(-0.7660) + 30°) / 2
Using a calculator to approximate arccos(-0.7660):
θ ≈ (40.607° + 30°) / 2
θ ≈ 70.607° / 2
θ ≈ 35.3035°
Therefore, the solution for theta is approximately 35.3035°.
To solve for theta in the equation cos(2theta-30 degrees) = -0.7660, we can follow these steps:
Step 1: Rewrite -0.7660 as cos inverse value:
cos inverse (-0.7660) = 141.69 degrees
Step 2: Set up the equation:
2theta - 30 degrees = 141.69 degrees
Step 3: Solve for theta:
2theta = 141.69 degrees + 30 degrees
2theta = 171.69 degrees
theta = 171.69 degrees / 2
theta = 85.84 degrees
So, the solution for theta in the given equation is approximately 85.84 degrees.