Question

Find sin X, cos X, and tan X as
a fraction in simplest form.

Answer 1

sin X = 4/5, or 0.8

cos X = 3/5, or 0.6

tan X = 4/3, or 1.333...

Explanation:

Recall that where "o" ≡ "opposite side", "a" ≡ "adjacent side" and "h" ≡ "hypotenuse", then we have three definitions for those function

sin = o/h

cos = a/h

tan = o/a

Before solving two of these then, we'll need to know the length of the hypotenuse, so we'll apply the Pythagorean theorem to find it:

a² = b² + c²

h² = 24² + 18²

h = √(576 + 324)

h = √900

h = 30

So for X, the sine is the length of the opposite side, divided by the length of the hypotenuse, or 24/30:

24 / 30

= 4 / 5

= 0.8

The cosine of x is:

18 / 30

= 3 / 5

= 0.6

Finally the tan of x is:

24 / 18

4 / 3

1.333...

Answer 2

sin X =
`(4)/(5)`

cos X =
`(3)/(5)`

tan X =
`1(1)/(3)`

Explanation:

First, find what the hypothenuse is:

`c^(2) = a^(2) + b^(2)`

`c^(2) = 18^(2) + 24^(2)`

`c^(2) = 324 + 576`

`\sqrt{c^(2)} = √(900)`

c = 30

`sine = (opposite)/(hypothenuse)\\\\`

sin x =
`(24)/(30) = (4)/(5)`

`cosine = (adjacent)/(hypothenuse)`

cos x =
`(18)/(30) = (3)/(5)`

`tan = (opposite)/(adjacent)`

tan x =
`(24)/(18) = 1(6)/(18) = 1(1)/(3)`