if sin a=4/5 and is quadrant 2 and sin b= 8/17 and is in quadrant 1, find cos (a-b)
To find cos(a-b), we first need to know the values of cos(a) and cos(b). However, we are only given the values of sin(a) and sin(b).
To find cos(a) and cos(b), we can use the Pythagorean identity, which states that sin^2(x) + cos^2(x) = 1.
For sin(a) = 4/5 in quadrant 2, we can calculate cos(a) as follows:
cos(a) = √[1 - sin^2(a)]
= √[1 - (4/5)^2]
= √[1 - 16/25]
= √[9/25]
= 3/5
For sin(b) = 8/17 in quadrant 1, we can calculate cos(b) as follows:
cos(b) = √[1 - sin^2(b)]
= √[1 - (8/17)^2]
= √[1 - 64/289]
= √[225/289]
= 15/17
Now that we have cos(a) = 3/5 and cos(b) = 15/17, we can proceed to find cos(a-b) using the formula:
cos(a-b) = cos(a) * cos(b) + sin(a) * sin(b)
Substituting in the values we obtained earlier:
cos(a-b) = (3/5) * (15/17) + (4/5) * (8/17)
= 45/85 + 32/85
= (45+32)/85
= 77/85
Therefore, cos(a-b) = 77/85.