Q:

Find sin and tan (Picture provided)

Accepted Solution

A:
Answer:Option C. [tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex] , [tex]tan(\theta)=-\frac{\sqrt{33}}{4}[/tex]Step-by-step explanation:we know thatIf cosine of angle theta is positive  then angle theta belong to the I or IV quadrantand If co secant of angle theta is negative then angle theta belong to the III or IV quadrantthereforeangle theta belong to the IV quadrant (common solution)Part 1) Find [tex]sin(\theta)[/tex]we know that[tex]sin^{2} (\theta)+cos^{2} (\theta)=1[/tex]we have[tex]cos(\theta)=4/7[/tex]substitute the value[tex]sin^{2}(\theta)=1-(4/7)^{2}[/tex] [tex]sin^{2}(\theta)=1-(16/49)[/tex]  [tex]sin^{2}(\theta)=(33/49)[/tex][tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex] ----> is negative because the angle belong to the IV quadrantPart 2) Find [tex]tan(\theta)[/tex]we know that[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]we have[tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex][tex]cos(\theta)=4/7[/tex]substitute the values[tex]tan(\theta)=\frac{-\frac{\sqrt{33}}{7}}{4/7}[/tex][tex]tan(\theta)=-\frac{\sqrt{33}}{4}[/tex]