Answer:
Part A) Use the identity [tex]tan^2(A)+1=sec^2(A)[/tex]
Part B) [tex]cot(A)=-\frac{3\sqrt{7}}{7}[/tex]
Step-by-step explanation:
we know that
[tex]tan^2(A)+1=sec^2(A)[/tex] ----> by trigonometric identity
we have
[tex]sec(A)=\frac{4}{3}[/tex]
substitute in the expression above
[tex]tan^2(A)+1=(\frac{4}{3})^2[/tex]
solve for tan(A)
[tex]tan^2(A)+1=\frac{16}{9}[/tex]
[tex]tan^2(A)=\frac{16}{9}-1[/tex]
[tex]tan^2(A)=\frac{7}{9}[/tex]
square root both sides
[tex]tan(A)=\pm\frac{\sqrt{7}}{3}[/tex]
Remember that Angle A terminates in quadrant IV
so
The value of tan(A) is negative
[tex]tan(A)=-\frac{\sqrt{7}}{3}[/tex]
Find the value of cot(A)
we know that
[tex]cot(A)=\frac{1}{tan(A)}[/tex] ----> is the reciprocal
therefore
[tex]cot(A)=-\frac{3}{\sqrt{7}}[/tex]
simplify
[tex]cot(A)=-\frac{3\sqrt{7}}{7}[/tex]
