# Thread: FIND A and B

1. ## FIND A and B

Use an addition or subtraction formula to write the expression as a trigonometric function of one number:
.

I figured out A to = 3 and B to = 1.99
Only one of my two answer is correct I don't know which one?

2. ## Re: FIND A and B

The "difference formula" for cosine is $\displaystyle cos(x- y)= cos(x)cos(y)+ sin(x)sin(y)$. Here, $\displaystyle x= \frac{3\pi}{7}$ and $\displaystyle y= \frac{2\pi}{21}$. So $\displaystyle x- y= =\frac{3\pi}{7}-\frac{2\pi}{21}= \frac{9\pi- 2\pi}{21}= \frac{7\pi}{21}= \frac{\pi}{3}$. I don't know where you got "$\displaystyle \frac{1.99}{2}$" but $\displaystyle \frac{\pi}{3}$ radians is 60 degrees. Draw an equilateral triangle with each side of length s and drop a perpendicular from one vertex to one side. That divides the triangle into two right triangles having hypotenuse of length s and one leg, the one at the 60 degree angle, of length (1/2)s. The cosine is "near side over hypotenuse", $\displaystyle \frac{(1/2)s}{s}= \frac{1}{2}$, NOT $\displaystyle \frac{1.99}{2}$.