Question

If sin y° = 9 divided by c. and tan y° = 9 divided by d. ,what is the value of cos y°?

Answer 1

recall your SOH CAH TOA \(\bf {\color{brown}{ sin}}(\theta)
=\cfrac{1}{csc(\theta)}
\\ \quad \\

% cosine
{\color{blue}{ cos}}(\theta)
=\cfrac{1}{sec(\theta)}
\\ \quad \\

% tangent
tan(\theta)
=\cfrac{{\color{brown}{ sin}}(\theta)}{{\color{blue}{ cos}}(\theta)}\)

thus we know that \(\bf sin(y^o)=\cfrac{9}{c}\qquad tan(y^o)=\cfrac{9}{d}\qquad thus
\\ \quad \\
tan(\theta)
=\cfrac{{\color{brown}{ sin}}(\theta)}{{\color{blue}{ cos}}(\theta)}\implies \cfrac{9}{d}=\cfrac{\frac{9}{c}}{cos(y^o)}\impliedby \textit{solve for }cos(y^o)\)