Given:
Angle "x" is:
[tex]x=-\frac{14\pi}{3}[/tex]Find-:
1)
Reference angle of "x"
2)
The exact value of sinx, tanx, and secx
Explanation-:
Angle in degree,
[tex]\begin{gathered} x=-\frac{14\pi}{3} \\ \\ 1\text{ radian }=\frac{180}{\pi}\text{ degree} \\ \\ -\frac{14\pi}{3}\text{ radian }=\frac{180}{\pi}\times-\frac{14\pi}{3} \\ \\ =-840 \end{gathered}[/tex]So, the reference angle is:
[tex]\begin{gathered} \text{ Reference angle }=60\text{ } \\ \\ \text{ Angle in }3^{rd}\text{ Quadrant} \end{gathered}[/tex]2)
The exact value of,
[tex]\begin{gathered} \sin x \\ \\ \tan x \\ \\ \sec x \end{gathered}[/tex][tex]\begin{gathered} \sin x=\sin(-840) \\ \\ \text{ Refrenace angel 60 then the value is:} \\ \\ \text{ In }3^{rd}\text{ Quadrant,}\sin\text{ value is negative} \\ \\ =-\sin60 \\ \\ =-\frac{\sqrt{3}}{2} \end{gathered}[/tex]Value of tanx
[tex]\begin{gathered} \tan x=\tan(-840) \\ \\ \text{ Reference value 60 and value positive in 3 quadrant,} \\ \\ =\tan60 \\ \\ =\sqrt{3} \end{gathered}[/tex]Value of secx
[tex]\begin{gathered} \sec x=\sec(-840) \\ \\ =-\sec(60) \\ \\ =-2 \end{gathered}[/tex]