First we need to set this ratio up in the coordinate plane. Because this is tangent, the 3 goes opposite the reference angle and the 4 goes along the x-axis, adjacent to the reference angle. We see that we are missing the third side of the triangle when we do this, namely the hypotenuse. We use Pythagorean's Theorem to find that this side is 5. Now we have to deal with the identities for each sin(2A) and cos(2A).

sin(2A) = 2sin(A)cos(A)

We know from the triangle we drew in the coordinate plane that

$sin(A)=\frac{3}{5}$ and $cos(A)=\frac{4}{5}$ so we fill in the formula accordingly and then simplify:

$sin(2A)=2(\frac{3}{5})(\frac{4}{5})=\frac{24}{25}$

cos(2A) has 3 identities; I just picked the one I thought would be easiest to use and went with that one. Regardless of which one you pick you will get the same answer as long as you do the math correctly.

$cos(2A)=cos^2(A)-sin^2(A)$ and filling in the formula:

$cos(2A)=(\frac{4}{5})^2-(\frac{3}{5})^2\\cos(2A)=\frac{16}{25}-\frac{9}{25}\\cos(2A)=\frac{7}{25}$

I'm not sure why you have 7/2 there...

8 0

3 years ago

Ten people were chosen at random and surveyed. The survey asked participants for the number of hours they sleep per night

ddd [48]

Answer:

b is the answer of the question

5 0

4 years ago