Question

Let , −5−6 be a point on the terminal side of θ . find the exact values of cosθ , cscθ , and tanθ .

Answer 1

Given that point (-5, -6) is a point on the terminal side of θ. Since both the x coordinate and the y-coordinate are negative, θ is in the third quadrant.

The side opposite θ is -6 and the side adjacent θ is -5.

The hypothenus is given by $\sqrt{(-6)^+(-5)^2}=\sqrt{36+25}=\sqrt{61}$

The exact value of cosθ is given by:

$\cos\theta= \frac{adjacent}{hypothenuse} = \frac{-5}{\sqrt{61}}$

The exact value of cscθ is given by:

$\csc\theta= \frac{hypothenuse}{opposite} = \frac{\sqrt{61}}{-6}$

The exact value of tanθ is given by:

$\tan\theta= \frac{opposite}{adjacent} = \frac{-6}{-5} =1.2$