Question

if segment OU=1. Prove that Tan(alpha)=Sin(alpha)/Cos(alpha).

Answer 1

The plot is attached

Answer 2

Any idea how to do that?

Answer 3

use definitions of sin, cos, and tan
sin = opposite/hypotenuse
cos =adjacent/hypotenuse
tan = opposite/adjacent
substitute the appropriate lengths and you will see that tan = sin/cos

Answer 4

but what is the meaning of tan(alpha) and sen(alpha) in the graph. That confuses me

Answer 5

i think it comes from unit circle. if OA=1 then the vertical line AA'=sin(alpha) and OA'=cos(alpha)

Answer 6

In the lower side of the triangle I also have a cos(alph).

Answer 7

We dont know OA. We know that OU is 1

Answer 8

because AA' = sin(alpha) then we can assume OA=1because sin = opp/hypotenuse = AA'/OA = AA' -->therefore OA=1

Answer 9

clear. Going to try now

Answer 10

:)

Answer 11

Im not sure is what I did is righ. Please check it out for me:

Tan(alpha)=TU/OU (1)

if
sin(alpha)=TU/OT, then TU=OTSen(alpha) (2)
cos(alpha)=OU/OT, then OU=OTCos(alpha) (3)

replacing TU and OU in equation 1, I got

Tan(alpha)=Sen(alpha)/Cos(alpha)

Is that correcto?

Answer 12

yes very good