I accidently posted this in the Pre-Calc section, if possible can someone delete that?
How do I solve these
Cos^2x + 2sinxcosx - sin^2 x = 0 [0, 360)
sin(x +1) = cos x [0, 360)
Cos 4X - Cos 2X = 0 but range is [-180, 180]
And finally
Logan has a garden in the shape of a sector of a circle; outer rim of garden is 25 ft long and central angle along of sector is 50 degrees, she wants to add a 3 ft wide walk to the outer rim, how many sq ft of paving does she need to build it?
Worded problem:
First, you need to find the radius of this sector.
To do this, remember that .
In your case, since your angle is , this means you have of the circle.
So you have
.
You know that this part of the circumference is .
So
.
Now, you are planning to make a path around the outside of this sector.
If you draw it, you'll notice that you have a sector inside a sector.
The first sector has radius , and since the pavers are wide, the second sector has radius .
.
.
.
So
.
It should be
Cos 4X - Cos 2X = 0 but range is [-180, 180]
And prove it, your answers don't seem to correlate to the answers in the back of the book which says:
3pi\8, 7pi\8, 11pi\8 and 15pi\8 for the first one
and .285, 3.427 for the second
And answer to the last should be 121 square ft