Find the six trigonometric functions are positive for $x = \frac{10 π}{3}$ ?

Open in App

Solution

REF.Image.
$a r c (\frac{10 π}{3}) = a r c (2 π + \frac{4 π}{3}) = a r c (\frac{4 π}{3})$
on the trigonometric unit circle.
$s i n (\frac{4 π}{3}) = s i n (π + \frac{π}{3}) = - s i n \frac{π}{3} = - \frac{\sqrt{3}}{2}$
$c o s (\frac{4 π}{3}) = c o s (π + \frac{π}{3}) = - c o s - \frac{π}{3} = - \frac{1}{2}$
$t a n (\frac{4 π}{3}) = \frac{s i n (\frac{4 π}{3})}{c o s (\frac{4 π}{3})} = \frac{- \sqrt{3} / 2}{- 1 / \sqrt{3}} = \sqrt{3}$
$c o t (\frac{4 π}{3}) = \frac{1}{t a n (\frac{4 π}{3})} = \frac{1}{\sqrt{3}}$
$s e c (\frac{4 π}{3}) = \frac{1}{c o s (\frac{4 π}{3})} = \frac{1}{\frac{- 1}{2}} = - 2$
$c o s e c (\frac{4 π}{3}) = \frac{1}{s i n (\frac{4 π}{3})} = \frac{+ 1}{\frac{- \sqrt{3}}{2}} = \frac{- 2}{\sqrt{3}}$

Suggest Corrections

Similar questions

\frac{11 x}{3}

\frac{e^{x} - e^{- x}}{2}

x ϵ R

x

sinh x

cosh x = \frac{e^{x} + e^{- x}}{2}

x

x

tanh x = \frac{sinh x}{cosh x}

cosech x = \frac{1}{sinh x}, coth x = \frac{1}{tanh x}

θ

cot x = \frac{3}{4}, x

s i n \frac{{2 π}^{c}}{3}

Join BYJU'S Learning Program