Trigonometric Equations

Step 1: Convert to decimal degrees: Step 2: Convert to radians: Step 3: Use the approximation for near , or directly calculate using a calculator: Thus, the approximate value of is:

We are given the equation: Step 1: Use sum-to-product identities. Recall the identity: We apply this identity to : So, the original equation becomes: Step 2: Factor out : Step 3: Solve for and : Thus, the general solution is:

We are given and need to prove that it equals . Step 1: Let . Then, by the definition of the inverse sine function: Step 2: We know that is the angle whose cosine is . Therefore, we have: Step 3: Therefore: Thus, the equation is proved.

Step 1: Finding the General Solutions
The equation holds at: Step 2: Principal Solutions
The general solutions in the principal range are: