Question

(10.05 LC)

If sin(x) =½
what is cos(x) and tan(x)? Explain your steps in complete sentences. (10 points)
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Answer 1

Cos x =
`(base)/(hypotenuse)=(√(3) )/(2)`

Tan x =
`(perpendicular)/(base) = (1)/(√(3) )`

Explanation:

Sin x =
`(perpendicular)/(hypotenuse) = (1)/(2)`

So, Perp = 1 and hyp = 2

Putting this in Pythagorean theorem to get the base

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

`a^2 = c^2-b^2`

base ² = 4-1

base² = 3

Taking square root on both sides

Base =
`√(3)`

Now

Cos x =
`(base)/(hypotenuse)=(√(3) )/(2)`

Tan x =
`(perpendicular)/(base) = (1)/(√(3) )`