I posted this earlier today:
I do not know how to find a single function of x or ø by using an identity. How do you find a single function using identities for a problem such as:
cos(3pi/4 - x)
But I think either I'm trying to find ø or I'm trying to find what x equals. I just sincerely do not know what to do with these problems.
Both Steve and I both told you what was wrong with the wording of the question.
http://www.jiskha.com/display.cgi?id=1480115359
Did you even look at the responses?
I suggest you post the problem exactly as it was given to you. If it's just part of an exercise set, include the instructions that preceded the section containing the problem.
Finding a single function of x or ø using identities involves simplifying the expression using trigonometric identities until you can express it as a single function. In the case of cos(3π/4 - x), we can use the trigonometric identity for the cosine of the difference of two angles:
cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
To simplify cos(3π/4 - x), let's first rewrite it using the identity mentioned above:
cos(3π/4 - x) = cos(3π/4)cos(x) + sin(3π/4)sin(x)
Now, we need to determine the values of cos(3π/4) and sin(3π/4). To do that, recall the unit circle. At 3π/4 radians (or 135 degrees), the coordinates on the unit circle are:
cos(3π/4) = -√2/2
sin(3π/4) = √2/2
Substituting these values, we get:
cos(3π/4 - x) = (-√2/2)cos(x) + (√2/2)sin(x)
At this point, we have expressed cos(3π/4 - x) as a single function of x, namely:
f(x) = (-√2/2)cos(x) + (√2/2)sin(x)
This is the desired result. You can now use this function to evaluate cos(3π/4 - x) for any given value of x.