Question

Given that sinθ=a/b,then find cosθ.

Answer 1

given sin x =a/b

means opposite/hypotenuse=a/b

opp=a

hypo=b

now from formula of phytogaros theorem hypo*2=opp*2+adj*2

b*2=a*2+adj*2

b*2-a*2=adj*2

√b*2-a*2=adj

we know that cosx=adjacent/hypotenuse

adj=√b*2-a*2

hypo=a

so from above we say that cosx=√b*2-a*2/b

we can also proof b*2=a*2+b*2-a*2