Question

Find the trigonometric functions of :

330°

Answer 1

Trigonometric Functions of 330° :

Let measure of ∠XOA in standard position be 330°.

Its terminal arm (ray OA) intersects the standard unit circle in P (x, y), which lies in the fourth quadrant.

Draw segment PM perpendicular to the X-axis.

∴ ΔOMP is a 30° – 60° – 90° triangle.

Op = 1.

OM = ${\displaystyle \frac{\sqrt{3}}{2}\text{OP}}$

= ${\displaystyle \frac{\sqrt{3}}{2}\left(1\right)}$

= ${\displaystyle \frac{\sqrt{3}}{2}}$

PM = ${\displaystyle \frac{1}{2}\text{OP}}$

= ${\displaystyle \frac{1}{2}\left(1\right)}$

= ${\displaystyle \frac{1}{2}}$

Since point P lies in the 4^th quadrant,

x > 0, y < 0

∴ x = OM = ${\displaystyle \frac{\sqrt{3}}{2}\text{and}y=-\text{PM}=-\frac{1}{2}}$

∴ P ≡ ${\displaystyle (\frac{\sqrt{3}}{2},\frac{-1}{2})}$

sin 330° = y = ${\displaystyle -\frac{1}{2}}$

cos 330° = x = ${\displaystyle \frac{\sqrt{3}}{2}}$

tan 330° = ${\displaystyle \frac{y}{x}=\frac{-\frac{1}{2}}{\frac{\sqrt{3}}{2}}=-\frac{1}{\sqrt{3}}}$

cosec 330° = ${\displaystyle \frac{1}{y}=\frac{1}{(-\frac{1}{2})}}$ = – 2

sec 330° = ${\displaystyle \frac{1}{x}=\frac{1}{\left(\frac{\sqrt{3}}{2}\right)}=\frac{2}{\sqrt{3}}}$

cot 330° = ${\displaystyle \frac{x}{y}=\frac{\frac{\sqrt{3}}{2}}{-\frac{1}{2}}=-\sqrt{3}}$