Question

Find cosθ, cscθ, and tanθ, where θ is the angle shown in the figure. Give exact values, not decimal approximations.

Answer 1

Answer:

see explanation

Step-by-step explanation:

To find cscθ we require to find the third side of the triangle.

let 3rd side be x and using Pythagoras' identity

x² + 8² = 9²

x² + 64 = 81 ( subtract 64 from both sides )

x² = 17 ( take square root of both sides )

x = $\sqrt{17}$

Then

cosθ = $\frac{adjacent }{hypotenuse}$ = $\frac{8}{9}$

cscθ = $\frac{hypotenuse}{opposite}$ = $\frac{9}{\sqrt{17} }$

tanθ = $\frac{opposite}{adjacent}$ = $\frac{\sqrt{17} }{8}$