Right △ABC has its right angle at C, BC=4 , and AC=8 .
What is the value of the trigonometric ratio?
sin A=
tan B=
sec A=
Start with drawing that right angle triangle
The sides are
BC=4
AC=8
AB=\(\sqrt{80}\) (applying Pythagoras theorem,
\(\sqrt{(AC)^2+(BC)^2}=AB\) "Addition since AB is the hypotenuse"
So we know the sides and they ask for trigonometric ratios
sin A =??
I assume A is angle "A"
\(sin(A)=\frac{opposite}{hypotenuse}\)
The opposite side to angle A is BC and the hypotenuse is AB
We know BC=4 and AB= \(\sqrt{80}\)
\(sin(A)=\frac{4}{\sqrt{80}}\)
Here is hints for the next 2 questions:
\(tan(B)=\frac{opposite}{adjacent}\)
\(sec(A)=\frac{hypotenuse}{adjacent}\)Proof: (Notice that \(sec(A)=\frac{1}{cos(A)}\), we know that \(cos(A)=\frac{Adjacent}{Hypotenuse}\) , substitute: \(sec(A)=\frac{1}{\frac{adjacent}{hypotenuse}}\) Multiply the numerator and denominator by the hypotenuse, \(sec(A)=\frac{hypotenuse}{adjacent}\)