Question

8.

When I take sine 45 and divide it by cosine 45, does it equal to tangent 45? Why is it equal? Does sine an angle
divided by cosine an angle always to tangent the angle? Why or why not?

Answer 1

See below

Explanation:

It is a trigonometric identity that
`(sin\theta)/(cos\theta)=tan\theta`.

Why is this the case? Let's think back to definitions:

`sin\theta=(opposite)/(hypotenuse)`

`cos\theta=(adjacent)/(hypotenuse)`

`tan\theta=(opposite)/(adjacent)`

So,
`(sin\theta)/(cos\theta)=((opposite)/(hypotenuse) )/((adjacent)/(hypotenuse) )=(opposite)/(hypotenuse)*(hypotenuse)/(adjacent)=(opposite)/(adjacent)=tan\theta`.