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Answer:
The solutions on the given interval are :
Step-by-step explanation:
We will need the double angle identity .
Let's begin:
Use double angle identity mentioned on left hand side:
Simplify a little bit on left side:
Subtract on both sides:
Factor left hand side:
Set both factors equal to 0 because at least of them has to be 0 in order for the equation to be true:
The first is easy what angles are
-coordinates on the unit circle 0. That happens at
and
on the given range of
(this
is not be confused with the
-coordinate).
Now let's look at the second equation:
Isolate .
Add 1 on both sides:
Divide both sides by 4:
This is not as easy as finding on the unit circle.
We know will render us a value between
and
.
So one solution on the given interval for x is .
We know cosine function is even.
So an equivalent equation is:
Apply to both sides:
Multiply both sides by -1:
This going to be negative in the 4th quadrant but if we wrap around the unit circle, , we will get an answer between
and
.
So the solutions on the given interval are :