Question

Calculate the six trigonometric function values of an angle θ in standard position whose terminal side goes through the point (−12,16). Make sure your fractions are fully reduced.

Answer 1

GIven:

$x=-12\text{ ;y=16}$$\begin{gathered} r=\sqrt[]{x^2+y^2} \\ r=\sqrt[]{(-12)^2+(16)^2} \\ r=\sqrt[]{144+256} \\ r=\sqrt[]{400} \\ r=20 \end{gathered}$$\begin{gathered} \sin \theta=\frac{y}{r} \\ \sin \theta=\frac{16}{20} \\ \sin \theta=\frac{4}{5} \end{gathered}$$\begin{gathered} \cos \theta=\frac{x}{r} \\ \cos \theta=-\frac{12}{20} \\ \cos \theta=-\frac{3}{5} \end{gathered}$$\begin{gathered} \tan \theta=\frac{y}{x} \\ \tan \theta=-\frac{16}{12} \\ \tan \theta=-\frac{4}{3} \end{gathered}$$co\sec \theta=\frac{5}{4}$$\sec \theta=-\frac{5}{3}$$\cot \theta=-\frac{3}{4}$