Question

If sin θ = `(8)/(17)`, find the other five trigonometric ratios.

Answer 1

sin θ  = `(8)/(17) = "Perpendicular"/"Hypotenuse"`

Base
= `sqrt(("Hypotenuse")^2 - ("Perpendicular")^2`
= `sqrt(17^2 - 8^2)`
= `sqrt(225)`
= 15

cos θ  = `"Base"/"Hypotenuse" = (15)/(17)`

tan θ  = `"Perpendicular"/"Base" = (8)/(15)`

cosecθ  = `(1)/"sin θ" = (17)/(8)`

sec θ  = `(1)/"cos θ " = (17)/(15)`

cot θ  = `(1)/"tan θ " = (15)/(8)`.