Question

Given that cosθ=7/25 , what is sinθ ?
no clue on how to solve this one.
fraction please.

Answer 1

`\Large \boxed{\sf sin \theta=(24)/(25)} \\\\\\\sf \displaystyle cos \theta=(adj)/(hyp) =(7)/(25) \\\\adj=7\ and\ hyp=25 \\\\Use\ the\ Pythagorean\ theorem\\\\opp=√(hyp^2-adj^2) =√(25^2-7^2) =24 \\\\sin \theta=(opp)/(hyp) =(24)/(25)`

Answer 2

you need to use the definitions of sin and cos

`sinx = (opp)/(hyp) \\ cosx = (adj)/(hyp)`from the question adj=7 ,hyp=25
since sin and cos are defined for a right triangle then

`{opp}^(2) + {adj}^(2) = {hyp}^(2)`
solving for opp so we can find sin

`opp = \sqrt{ {hyp}^(2) - {adj}^(2) }`
so plugging in the numbers

`opp = \sqrt{ {25}^(2) - {7}^(2) } = √(625 - 49) = √(576) = 24`

therefore

`sin(x) = (opp)/(hyp) = (24)/(25)`