# Thread: Find the indicated trigonometric function given that...

1. ## Find the indicated trigonometric function given that...

... (theta) is an angle in standard position with the terminal side passing through the given point.

(-7,-3); Find sec(theta).

(15,20); Find csc(theta).

(6,-8); Find cot(theta).

I really wish I was good at maths.

2. ## Re: Find the indicated trigonometric function given that...

I'll do the first one . . .

$\displaystyle \theta$ is an angle in standard position with the terminal side passing through the given point.

. . $\displaystyle (\text{-}7,\text{-}3);\;\text{ Find }\sec\theta$

We are given: .$\displaystyle \begin{Bmatrix}x &=& \text{-}7 \\ y &=& \text{-}3 \end{Bmatrix}$

. . and: .$\displaystyle r \:=\:\sqrt{x^2+y^2} \:=\:\sqrt{(\text{-}7)^2 + (\text{-}3)^2} \:=\:\sqrt{58}$

Then we have these definitions: .$\displaystyle \begin{Bmatrix}\sin\theta \:=\:\dfrac{y}{r} && \csc\theta \:=\:\dfrac{r}{y} \\ \\[-3mm] \cos\theta \:=\:\dfrac{x}{r} && \sec\theta \:=\:\dfrac{r}{x} \\ \\[-3mm] \tan\theta \:=\:\dfrac{y}{x} && \cot\theta \:=\:\dfrac{x}{y} \end{Bmatrix}$

Can you finish the problem now?

3. ## Re: Find the indicated trigonometric function given that...

(square root)58/-7 ! Yes! Thank you so much!