Question

Let tan x = 2.4, sin y = 0.6, and both x and y be between 0° and 90°. Then cos(x + y) equals?

Answer 1

`- frac{16}{65}`

Explanation:

Answer 2

cos (x + y) = - 0.246

Explanation:

Use trig identity:
cos (x + y) = cos x.cos y - sin x.sin y (1)
First, find cos y knowing sin y = 0.6
`cos^2 y = 1 - sin^2 y = 1 - 0.36 = 0.64`
`cos y = 0.8` (because y is in Quadrant 1)
Next, find sin x and cos x, knowing tan x = 2.4.
`cos^2 x = 1/(1 + tan^2 x) = 1/(1 + 5.76) = 1/6.76`
`cos x = 1/2.6` (because x is in Q. 1)
`sin^2 x = 1 - cos^2 x = 1 - 1/6.76 = 5.76/6.76`
`sin x = 2.4/2.6`
Replace all numeric values into equation (1), we get:
`cos (x + y) = (1/2.6)(0.8) - (2.4/2.6)(0.6) = 0.8/2.6 - 1.44/2.6`
`cos (x + y) = - 0.64/2.6 = - 0.246`
Check by calculator.
`sin y = 0.6` --> `y = 36^@87`
`cos x = 1/2.6` --> `x = 67^@38`
`x + y = 36.87 + 67.38 = 104^@25` --> cos 104.25 = - 0.246. OK