If it is not clear if the answer is radians or degrees, we will start with radians, since there is no degree symbol in the number 10 inside the sine function.
so we want the cos of an angle to be equal to the sin of another angle which is the modified version of the original angle theta.
We try using the expression for the sin of a difference.
sin( A - B) = sin(A) cos(B) - cos(A) sin(B)
It looks like the answer is straight forward for the case of degrees. So let's use degrees.
So we set the graphing tool in "degrees", and use the graphing of two functions separately, looking for the intersection of the graphs.
We get the following first intersection:
where the trace in blue is that of the cosine function, and the orange one that of the sin function. The intersection takes place place at the angle theta = 75 degrees.
We also look at any other intersection further down the graph, since these functions are periodic and can repeat values.
The next two intersections take place at theta = 345 degrees and at 390 degrees.
If the problem is asking for solutions in a given interval (normally they ask between 0 and 360 degrees), you need to give just the first two intersections we found: 75 degrees and 345 degrees.
Do you have a restricted interval for the solutions?
Or they may give you a list of values to select from. Recall that there are going to be INFINITE number of solutions since the functions are periodic.
Can you check your answer right now?
