Question

Find cos(x+y) if sin(x)=(3)/(5), cos(y)=(1)/(4),x is in quadrant 2, and y is in quadranrt 3

Answer 1

To find cos(x+y), use trigonometric identities and given information. Calculate cos(x) using the Pythagorean identity and then use the cos(a + b) identity to find cos(x+y).

Step-by-step explanation:

To find cos(x+y), we need to use the trigonometric identities and given information. Since sin(x) = 3/5, we can find cos(x) using the Pythagorean identity: cos(x) = sqrt(1 - sin^2(x)) = sqrt(1 - (3/5)^2) = sqrt(1 - 9/25) = sqrt(16/25) = 4/5.

Next, we can use the given information that cos(y) = 1/4. Now, we can use the trigonometric identity: cos(a + b) = cos(a)cos(b) - sin(a)sin(b). Plugging in the values, we get cos(x+y) = cos(x)cos(y) - sin(x)sin(y) = (4/5)(1/4) - (3/5)(1/4) = 4/20 - 3/20 = 1/20.