Answer:
[tex]\displaystyle \large{\cos \theta = \dfrac{-3}{\sqrt{34}} = -\dfrac{3\sqrt{34}}{34}}\\\\\displaystyle \large{\csc \theta = \dfrac{\sqrt{34}}{5}}\\\\\displaystyle \large{\tan \theta = -\dfrac{5}{3}}[/tex]
Step-by-step explanation:
Accorded to trigonometric formula, we know that:
[tex]\displaystyle \large{\cos \theta = \dfrac{x}{r}}\\\\\displaystyle \large{\csc \theta = \dfrac{1}{\sin \theta} = \dfrac{1}{\frac{y}{r}} = \dfrac{r}{y}}\\\\\displaystyle \large{\tan \theta = \dfrac{\sin \theta}{\cos \theta} = \dfrac{y}{x}}[/tex]
We know what x and y are but not yet knowing what r is. We can find r (radius) using the formula:
[tex]\displaystyle \large{r=\sqrt{x^2+y^2}}[/tex]
Input x = -3 and y = 5 in.
[tex]\displaystyle \large{r=\sqrt{(-3)^2+(5)^2}}\\\\\displaystyle \large{r=\sqrt{9+25}}\\\\\displaystyle \large{r=\sqrt{34}}[/tex]
Hence, radius is √34 and we know all we need now. Substitute x = -3, y = 5 and r = √34 in respective areas.
[tex]\displaystyle \large{\cos \theta = \dfrac{-3}{\sqrt{34}} = -\dfrac{3\sqrt{34}}{34}}\\\\\displaystyle \large{\csc \theta = \dfrac{\sqrt{34}}{5}}\\\\\displaystyle \large{\tan \theta = -\dfrac{5}{3}}[/tex]
These are the answers to your question. Please let me know if you have any questions regarding my answer or explanation!
