Question

List the six (6) trigonometric ratios for the angle 2(pi)/3 using the unit circle.

Answer 1

The six trigonometric ratios are
`sin(\theta)\\`,
`cos(\theta)`,
`tan(\theta)\\`,
`\csc{\theta}\\`,
`\sec{\theta}\\`,
`\cot{\theta}\\`

`\sin{(2\pi)/(3)} = \sin{(\pi)/(3)} = (√(3))/(2)\\\cos{(2\pi)/(3)} = \cos{(\pi)/(3)} = (1)/(2)\\\tan{(2\pi)/(3)} = \tan{(\pi)/(3)} = \frac{\sin{(\pi)/(3)}}{\cos{(\pi)/(3)}} = ((√(3))/(2))/((1)/(2)) = (2√(3))/(2) = √(3)\\\csc{(2\pi)/(3)} = \csc{(\pi)/(3)} = \frac{1}{\sin{(\pi)/(3)}} = (1)/((√(3))/(2)) = (2)/(√(3))} = (2√(3))/(3)\\`

`\sec{(2\pi)/(3)} = \sec{(\pi)/(3)} = \frac{1}{\cos{(\pi)/(3)}} = (1)/((1)/(2)) = (2)/(1) = 2\\\cot{(2\pi)/(3)} = \cot{(\pi)/(3)} = \frac{1}{\tan{(\pi)/(3)}} = (1)/(√(3)) = (√(3))/(3)`