Question

which of the six trigonometric functions are positive for x=-10π/3?​

Answer 1

Question:-

$\diamondsuit$ Which of the six trignometric functions are positive for x = $\frac{-10π}{3}$

Answer:-

$\implies$ arc $\bf \dfrac{10π}{3}$

$\implies$ arc $\dfrac({4π}{3}) \: + 2π$

= arc $\frac{4π}{3}$

Now on the trignometric unit circle

➡sin$\frac{4π}{3}$ = $- \frac{sinπ}{3} = -\frac{{\sqrt{3}{2}}$

➡cos$\frac{4π}{3}$ = $- \frac{cosπ}{3} = -\frac{1}{2}$

➡tan$\frac{4π}{3}$ = $\frac{sin}{cos} = \sqrt{3}$

➡cot$\frac{4π}{3}$ = $\frac{1}{{\sqrt{3}} = \frac{{\sqrt{3}}}{3}$

➡sec$\frac{4π}{3}$ = $-\frac{2}{{\sqrt{3}}} = \times{2} \frac{{\sqrt{3}}}{3}$

So all the values in functions of $\frac{10π}{3}$ came.