If tanØ=3/4 what is sinØ=

If tanØ=3/4 what is sinØ=?

\(\begin{array}{|rcll|} \hline \sin(\phi) = \frac35 \quad \text{or} \quad \sin(\phi) = -\frac35 \\ \hline \end{array}\)

sinØ=0,6

If tanØ=3/4 what is sinØ=

Sin(x) = tan(x) / [sqrt(1 + tan^2(x)] 

Sin(theta) =3/4 / sqrt[1 + .75^2]

Sin(theta) =0.75 / sqrt[ 1.5625 ]

Sin(theta) =0.75 / 1.25

Sin(theta) = 0.60

Tan = 3/4 = sin/cos      remember   sin^2 + cos^2 =1    and  sqrt(sin^2 + cos^2) = 1

sqrt (3^2 + 4^2) = 5     but it should equal ONE   so the num and denominator need to be reduce by a factor of 5

tan = 3/5  /  4/5     Now   sqrt(sin^2 + cos^2)  = 1      

also   1-cos^2 = sin^2

1-(4/5)^2 = sin^2

9/25 = sin^2           which means sin = 3/5   or - 3/5   (.6  or -.6)