FIND A and B

**M670** · November 12th 2012, 04:19 PM

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?

**HallsofIvy** · November 12th 2012, 04:42 PM

The "difference formula" for cosine is $cos(x- y)= cos(x)cos(y)+ sin(x)sin(y)$ . Here, $x= \frac{3\pi}{7}$ and $y= \frac{2\pi}{21}$ . So $x- y= =\frac{3\pi}{7}-\frac{2\pi}{21}= \frac{9\pi- 2\pi}{21}= \frac{7\pi}{21}= \frac{\pi}{3}$ . I don't know where you got " $\frac{1.99}{2}$ " but $\frac{\pi}{3}$ 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", $\frac{(1/2)s}{s}= \frac{1}{2}$ , NOT $\frac{1.99}{2}$ .

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