Hello! Let x=-14pi/3. Part A: Determine the reference angle of x with work shown. Part B: Find the exact values of sin x, tan x, and sec x in simplest form. Thank you!

Hello Let X14pi3 Part A Determine The Reference Angle Of X With Work Shown Part B Find The Exact Values Of Sin X Tan X And Sec X In Simplest Form Thank You class=

Answer :

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]