Question

Find the three trigonometric function values for the angle ø shown.

sin ø =
cos ø =
tan ø =

​

Answer 1

at ∠A sin Ф = 180 + (2 /
`√(22)` )

at ∠B cos Ф = 180 + (3
`√(2)` /
`√(22)` )

at ∠C tan Ф = 180 + (2 / 3
`√(2)` )

Explanation:

let (a) = 3
`√(2)`

let (b) = 2

let (c) = r

to get the value of hypotenuse (r) use pythagorean theorem

a² + b² = c²

2² + (3
`√(2)` )² = c²

c =
`√(22)`

use the law of sines to get the value of angle A (point origin)

sin Ф = opp / hyp

cos Ф = adj / hyp

tan Ф = opp / adj

at ∠A

sin Ф = 180 + (2 /
`√(22)` )

at ∠B

cos Ф = 180 + (3
`√(2)` /
`√(22)` )

at ∠C

tan Ф = 180 + (2 / 3
`√(2)` )