Question

If sin θ = ${\displaystyle \frac{8}{17}}$, find the other five trigonometric ratios.

Answer 1

sin θ  = ${\displaystyle \frac{8}{17}=\frac{\text{Perpendicular}}{\text{Hypotenuse}}}$

Base
= ${\displaystyle \sqrt{{\left(\text{Hypotenuse}\right)}^2-{\left(\text{Perpendicular}\right)}^2}}$
= ${\displaystyle \sqrt{{17}^2-8^2}}$
= ${\displaystyle \sqrt{225}}$
= 15

cos θ  = ${\displaystyle \frac{\text{Base}}{\text{Hypotenuse}}=\frac{15}{17}}$

tan θ  = ${\displaystyle \frac{\text{Perpendicular}}{\text{Base}}=\frac{8}{15}}$

cosecθ  = ${\displaystyle \frac{1}{\text{sin θ}}=\frac{17}{8}}$

sec θ  = ${\displaystyle \frac{1}{\text{cos θ}}=\frac{17}{15}}$

cot θ  = ${\displaystyle \frac{1}{\text{tan θ}}=\frac{15}{8}}$.