Question

Let (8,−3) be a point on the terminal side of θ. Find the exact values of cosθ, cscθ, and tanθ.

Answer 1

Answer:

$\text{Cos}\theta=\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{x}{R}=\frac{8}{\sqrt{73}}$

$\text{Csc}\theta=-\frac{\sqrt{73}}{3}$

$\text{tan}\theta =\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{y}{x}=\frac{-3}{8}$

Step-by-step explanation:

From the picture attached,

(8, -3) is a point on the terminal side of angle θ.

Therefore, distance 'R' from the origin will be,

R = $\sqrt{x^{2}+y^{2}}$

R = $\sqrt{8^{2}+(-3)^2}$

  = $\sqrt{64+9}$

  = $\sqrt{73}$

Therefore, Cosθ = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{x}{R}=\frac{8}{\sqrt{73}}$

Sinθ = $\frac{\text{Opposite side}}{\text{Hypotenuse}}=\frac{y}{R}=\frac{-3}{\sqrt{73} }$

tanθ = $\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{y}{x}=\frac{-3}{8}$

Cscθ = $\frac{1}{\text{Sin}\theta}=\frac{R}{y}=-\frac{\sqrt{73}}{3}$