Question

Fill in the blank. If necessary, use the slash mark ( / ) for a fraction bar.

If sin theta = 3/5, then cose theta = ?

Answer 1

cos Ф = adj / hyp could be either 4/5 or -4/5.

Explanation:

If sin Ф = 3/5, then we can assume that the opposite side is 3 and the hypotenuse is 5. Using the Pythagorean Theorem, we find that the adjacent side is 4:

√(5² - 3²) = √16 = ±4.

cos Ф = adj / hyp could be either 4/5 or -4/5.

Answer 2

`(4)/(5)`

Explanation:

Given,

`sin \theta = (3)/(5)`

`\because sin \theta =\frac{\text{Opposite side of }\theta}{\text{Hypotenuse }}`

By comparing,

Opposite side of
`\theta` = 3

Hypotenuse = 5,

By pythagoras theorem,

Adjacent side of
`\theta` =
`√(5^2 - 3^2)=√(25-9)=√(16)=4`

Now,

`cos \theta =\frac{\text{Adjacent side of }\theta}{\text{Hypotenuse }}`

`\implies cos \theta=(4)/(5)`