Answer:
1
Step-by-step explanation:
It is 5389.030 to nearest hundredth
Answer:
y=mx+b
Step-by-step explanation:
Answer:
Part 1) ![sin(A + B) =\frac{185}{697}](https://tex.z-dn.net/?f=sin%28A%20%2B%20B%29%20%3D%5Cfrac%7B185%7D%7B697%7D)
Part 2) ![sin(A - B) =\frac{455}{697}](https://tex.z-dn.net/?f=sin%28A%20-%20B%29%20%3D%5Cfrac%7B455%7D%7B697%7D)
Step-by-step explanation:
Suppose A is in Quadrant IV and B is in Quadrant III.
If cos(A)=(9/41) and cos(B)=-(8/17)
Part 1) Find sin(A+B)
step 1
Find sin(A)
we know that
![sin^2(A)+cos^2(A)=1](https://tex.z-dn.net/?f=sin%5E2%28A%29%2Bcos%5E2%28A%29%3D1)
we have
![cos(A)=\frac{9}{41}](https://tex.z-dn.net/?f=cos%28A%29%3D%5Cfrac%7B9%7D%7B41%7D)
substitute
![sin^2(A)+(\frac{9}{41})^2=1](https://tex.z-dn.net/?f=sin%5E2%28A%29%2B%28%5Cfrac%7B9%7D%7B41%7D%29%5E2%3D1)
![sin^2(A)+\frac{81}{1,681}=1](https://tex.z-dn.net/?f=sin%5E2%28A%29%2B%5Cfrac%7B81%7D%7B1%2C681%7D%3D1)
![sin^2(A)=1-\frac{81}{1,681}](https://tex.z-dn.net/?f=sin%5E2%28A%29%3D1-%5Cfrac%7B81%7D%7B1%2C681%7D)
![sin^2(A)=\frac{1,600}{1,681}](https://tex.z-dn.net/?f=sin%5E2%28A%29%3D%5Cfrac%7B1%2C600%7D%7B1%2C681%7D)
square root both sides
![sin(A)=\pm\frac{40}{41}](https://tex.z-dn.net/?f=sin%28A%29%3D%5Cpm%5Cfrac%7B40%7D%7B41%7D)
Angle A is in Quadrant IV
so
sine(A) is negative
therefore
![sin(A)=-\frac{40}{41}](https://tex.z-dn.net/?f=sin%28A%29%3D-%5Cfrac%7B40%7D%7B41%7D)
step 2
Find sin(B)
we know that
![sin^2(B)+cos^2(B)=1](https://tex.z-dn.net/?f=sin%5E2%28B%29%2Bcos%5E2%28B%29%3D1)
we have
![cos(B)=-\frac{8}{17}](https://tex.z-dn.net/?f=cos%28B%29%3D-%5Cfrac%7B8%7D%7B17%7D)
substitute
![sin^2(B)+(-\frac{8}{17})^2=1](https://tex.z-dn.net/?f=sin%5E2%28B%29%2B%28-%5Cfrac%7B8%7D%7B17%7D%29%5E2%3D1)
![sin^2(B)+\frac{64}{289}=1](https://tex.z-dn.net/?f=sin%5E2%28B%29%2B%5Cfrac%7B64%7D%7B289%7D%3D1)
![sin^2(B)=1-\frac{64}{289}](https://tex.z-dn.net/?f=sin%5E2%28B%29%3D1-%5Cfrac%7B64%7D%7B289%7D)
![sin^2(B)=\frac{225}{289}](https://tex.z-dn.net/?f=sin%5E2%28B%29%3D%5Cfrac%7B225%7D%7B289%7D)
square root both sides
![sin(B)=\pm\frac{15}{17}](https://tex.z-dn.net/?f=sin%28B%29%3D%5Cpm%5Cfrac%7B15%7D%7B17%7D)
Angle B is in Quadrant III
so
sine(B) is negative
therefore
![sin(B)=-\frac{15}{17}](https://tex.z-dn.net/?f=sin%28B%29%3D-%5Cfrac%7B15%7D%7B17%7D)
step 3
Find sin(A+B)
we know that
![sin(A + B) = sin A cos B + cos A sin B](https://tex.z-dn.net/?f=sin%28A%20%2B%20B%29%20%3D%20sin%20A%20cos%20B%20%2B%20cos%20A%20sin%20B)
we have
![sin(A)=-\frac{40}{41}](https://tex.z-dn.net/?f=sin%28A%29%3D-%5Cfrac%7B40%7D%7B41%7D)
![cos(A)=\frac{9}{41}](https://tex.z-dn.net/?f=cos%28A%29%3D%5Cfrac%7B9%7D%7B41%7D)
![cos(B)=-\frac{8}{17}](https://tex.z-dn.net/?f=cos%28B%29%3D-%5Cfrac%7B8%7D%7B17%7D)
![sin(B)=-\frac{15}{17}](https://tex.z-dn.net/?f=sin%28B%29%3D-%5Cfrac%7B15%7D%7B17%7D)
substitute
![sin(A + B) =(-\frac{40}{41})(-\frac{8}{17}) +(\frac{9}{41})(-\frac{15}{17})](https://tex.z-dn.net/?f=sin%28A%20%2B%20B%29%20%3D%28-%5Cfrac%7B40%7D%7B41%7D%29%28-%5Cfrac%7B8%7D%7B17%7D%29%20%2B%28%5Cfrac%7B9%7D%7B41%7D%29%28-%5Cfrac%7B15%7D%7B17%7D%29)
![sin(A + B) =\frac{320}{697} -\frac{135}{697}](https://tex.z-dn.net/?f=sin%28A%20%2B%20B%29%20%3D%5Cfrac%7B320%7D%7B697%7D%20-%5Cfrac%7B135%7D%7B697%7D)
![sin(A + B) =\frac{185}{697}](https://tex.z-dn.net/?f=sin%28A%20%2B%20B%29%20%3D%5Cfrac%7B185%7D%7B697%7D)
Part 2) Find sin(A-B)
we know that
![sin(A- B) = sin A cos B-cos A sin B](https://tex.z-dn.net/?f=sin%28A-%20B%29%20%3D%20sin%20A%20cos%20B-cos%20A%20sin%20B)
we have
![sin(A)=-\frac{40}{41}](https://tex.z-dn.net/?f=sin%28A%29%3D-%5Cfrac%7B40%7D%7B41%7D)
![cos(A)=\frac{9}{41}](https://tex.z-dn.net/?f=cos%28A%29%3D%5Cfrac%7B9%7D%7B41%7D)
![cos(B)=-\frac{8}{17}](https://tex.z-dn.net/?f=cos%28B%29%3D-%5Cfrac%7B8%7D%7B17%7D)
![sin(B)=-\frac{15}{17}](https://tex.z-dn.net/?f=sin%28B%29%3D-%5Cfrac%7B15%7D%7B17%7D)
substitute
![sin(A - B) =(-\frac{40}{41})(-\frac{8}{17}) -(\frac{9}{41})(-\frac{15}{17})](https://tex.z-dn.net/?f=sin%28A%20-%20B%29%20%3D%28-%5Cfrac%7B40%7D%7B41%7D%29%28-%5Cfrac%7B8%7D%7B17%7D%29%20-%28%5Cfrac%7B9%7D%7B41%7D%29%28-%5Cfrac%7B15%7D%7B17%7D%29)
![sin(A - B) =\frac{320}{697} +\frac{135}{697}](https://tex.z-dn.net/?f=sin%28A%20-%20B%29%20%3D%5Cfrac%7B320%7D%7B697%7D%20%2B%5Cfrac%7B135%7D%7B697%7D)
![sin(A - B) =\frac{455}{697}](https://tex.z-dn.net/?f=sin%28A%20-%20B%29%20%3D%5Cfrac%7B455%7D%7B697%7D)
1 should be b and 2 should be a