Answer:
Part 1) [tex]cos(\theta)=(\frac{13}{85})[/tex]
Part 2) [tex]tan(\theta)=\frac{84}{13}[/tex]
Part 3) [tex]cot(\theta)=\frac{13}{84}[/tex]
Part 4) [tex]sec(\theta)=\frac{85}{13}[/tex]
Part 5) [tex]csc(\theta)=\frac{85}{84}[/tex]
Step-by-step explanation:
we know that
Angle [tex]\theta[/tex] lie on Quadrant I
so
[tex]sin(\theta)[/tex] is positive
[tex]cos(\theta)[/tex] is positive
[tex]tan(\theta)[/tex] is positive
[tex]cot(\theta)[/tex] is positive
[tex]sec(\theta)[/tex] is positive
[tex]csc(\theta)[/tex] is positive
step 1
Find the value of [tex]cos(\theta)[/tex]
we have
[tex]sin(\theta)=\frac{84}{85}[/tex]
we know that
[tex]sin^2(\theta)+cos^2(\theta)=1[/tex]
substitute
[tex](\frac{84}{85})^2+cos^2(\theta)=1[/tex]
[tex](\frac{7,056}{7,225})+cos^2(\theta)=1[/tex]
[tex]cos^2(\theta)=1-(\frac{7,056}{7,225})[/tex]
[tex]cos^2(\theta)=(\frac{169}{7,225})[/tex]
[tex]cos(\theta)=(\frac{13}{85})[/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{84}{85}[/tex]
[tex]cos(\theta)=(\frac{13}{85})[/tex]
substitute
[tex]tan(\theta)=\frac{(84/85)}{(13/85)}[/tex]
[tex]tan(\theta)=\frac{84}{13}[/tex]
step 3
Find the value of [tex]cot(\theta)[/tex]
we know that
[tex]cot(\theta)=\frac{1}{tan(\theta)}[/tex]
we have
[tex]tan(\theta)=\frac{84}{13}[/tex]
therefore
[tex]cot(\theta)=\frac{13}{84}[/tex]
step 4
Find the value of [tex]sec(\theta)[/tex]
we know that
[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex]
we have
[tex]cos(\theta)=(\frac{13}{85})[/tex]
therefore
[tex]sec(\theta)=\frac{85}{13}[/tex]
step 5
Find the value of [tex]csc(\theta)[/tex]
we know that
[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]
we have
[tex]sin(\theta)=\frac{84}{85}[/tex]
therefore
[tex]csc(\theta)=\frac{85}{84}[/tex]
