Question

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

Answer 1

Answer:

sin X = $\frac{4}{5}$

cos X = $\frac{3}{5}$

tan X = $1\frac{1}{3}$

Step-by-step explanation:

First, find what the hypothenuse is:

$c^{2} = a^{2} + b^{2}$

$c^{2} = 18^{2} + 24^{2}$

$c^{2} = 324 + 576$

$\sqrt{c^{2}} = \sqrt{900}$

c = 30

$sine = \frac{opposite}{hypothenuse}$

sin x = $\frac{24}{30} = \frac{4}{5}$

$cosine = \frac{adjacent}{hypothenuse}$

cos x = $\frac{18}{30} = \frac{3}{5}$

$tan = \frac{opposite}{adjacent}$

tan x = $\frac{24}{18} = 1\frac{6}{18} = 1\frac{1}{3}$

Answer 2

Answer:

sin X = 4/5, or 0.8

cos X = 3/5, or 0.6

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

Step-by-step 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...