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

Find Cosθ Cscθ And Tanθ Where Θ Is The Angle Shown In The Figure Give Exact Values Not Decimal Approximations class=

Sagot :

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 = [tex]\sqrt{17}[/tex]

Then

cosθ = [tex]\frac{adjacent }{hypotenuse}[/tex] = [tex]\frac{8}{9}[/tex]

cscθ = [tex]\frac{hypotenuse}{opposite}[/tex] = [tex]\frac{9}{\sqrt{17} }[/tex]

tanθ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{\sqrt{17} }{8}[/tex]

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