Answer:
Part 1) [tex]sin(\theta)=-\frac{15}{17}[/tex]
Part 2) [tex]tan(\theta)=\frac{15}{8}[/tex]
Step-by-step explanation:
step 1
Find the value of
[tex]sin(\theta)[/tex]
we know that
[tex]sin^2(\theta)+cos^2(\theta)=1[/tex] ----> by trigonometric identity
we have
[tex]cos(\theta)=-\frac{8}{17}[/tex]
substitute
[tex]sin^2(\theta)+(-\frac{8}{17})^2=1\\\\sin^2(\theta)+\frac{64}{289}=1\\\\sin^2(\theta)=1-\frac{64}{289}\\\\sin^2(\theta)=\frac{225}{289}[/tex]
take square root both sides
[tex]sin(\theta)=-\frac{15}{17}[/tex]
step 2
Find the value of
[tex]tan(\theta)[/tex]
we know that
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
we have
[tex]sin(\theta)=-\frac{15}{17}[/tex]
[tex]cos(\theta)=-\frac{8}{17}[/tex]
substitute
[tex]tan(\theta)=\frac{15}{8}[/tex]
