Question
Find the trigonometric functions of : 120°
✓
Answer
Angle of measure $120^{\circ}$ : Let $m \angle X O A=120^{\circ}$ Its terminal arm (ray $O A$ ) intersects the standard unit circle at $P(x, y)$. Draw seg PM perpendicular to the $X$-axis. $\therefore \triangle O M P$ is a $30^{\circ}-60^{\circ}-90^{\circ}$ triangle. $O P=1$ Since point $P$ lies in the 2 nd quadrant, $x<0, y>0$
$ \therefore \quad x=-\mathrm{OM}=-\frac{1}{2} \text { and } y=\mathrm{PM}=\frac{\sqrt{3}}{2}$
$\therefore \quad \mathrm{P} \equiv\left(\frac{-1}{2}, \frac{\sqrt{3}}{2}\right)$
$\sin 120^{\circ}=y=\frac{\sqrt{3}}{2}$
$\cos 120^{\circ}=x=-\frac{1}{2}$
$\tan 120^{\circ}=\frac{y}{x}=\frac{\frac{\sqrt{3}}{2}}{-\frac{1}{2}}=-\sqrt{3}$
$\operatorname{cosec} 120^{\circ}=\frac{1}{y}=\frac{1}{\left(\frac{\sqrt{3}}{2}\right)}=\frac{2}{\sqrt{3}}$
$\sec 120^{\circ}=\frac{1}{x}=\frac{1}{\left(-\frac{1}{2}\right)}=-2$
$\cot 120^{\circ}=\frac{x}{y}=\frac{-\frac{1}{2}}{\frac{\sqrt{3}}{2}}=-\frac{1}{\sqrt{3}} $
[Note: Answer given in the textbook of $\tan 120^{\circ}$ is $\frac{-1}{\sqrt{3}}$ and $\cot 120^{\circ}$ is $-\sqrt{3}$.
However, as per our $-\sqrt{3}$ calculation the answer of $\tan 120^{\circ}$ is $-\sqrt{3}$ and $\cot 120^{\circ}$ is $-\frac{1}{\sqrt{3}}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find Minors and Cofactors of the elements of determinant
$\left|\begin{array}{lrr}1 & 2 & -3 \\ -2 & 0 & 4 \\ 5 & -1 & 3\end{array}\right|$
→$\left|\begin{array}{lrr}1 & 2 & -3 \\ -2 & 0 & 4 \\ 5 & -1 & 3\end{array}\right|$
Calculate the mean deviation about the median of the following observation:
$3011, 2780, 3020, 2354, 3541, 4150, 5000$
→$3011, 2780, 3020, 2354, 3541, 4150, 5000$
If $\sin\alpha+\sin\beta=\text{a}$ and $\cos\alpha+\cos\beta=\text{b},$ show that
$\cos(\alpha+\beta)=\frac{\text{b}^2-\text{a}^2}{\text{b}^2+\text{a}^2}$
→$\cos(\alpha+\beta)=\frac{\text{b}^2-\text{a}^2}{\text{b}^2+\text{a}^2}$
Find the equation to the ellipse in the following case:
eccentricity $\text{e}=\frac{1}{2}$ and semi-major axis = $4$
→eccentricity $\text{e}=\frac{1}{2}$ and semi-major axis = $4$
Show the following quadratic equation:
$\text{x}^2-(3\sqrt{2}-2\text{i})\text{x}-\sqrt{2}\text{ i}=0$
→$\text{x}^2-(3\sqrt{2}-2\text{i})\text{x}-\sqrt{2}\text{ i}=0$
$\cos 12^{\circ}+\cos 84^{\circ}+\cos 156^{\circ}+\cos 132^{\circ}=-\frac{1}{2}$
→Reduce the lines 3x - 4y - 4 = 0 and 2x + 4y - 5 = 0 to the normal form and hence find which line is nearer to the origin.
Differentiate the following from the first principle$\text{f}(\text{x})=\frac{\cos\text{x}}{\text{x}}$
→How many five-digit numbers formed using the digit 0, 1, 2, 3, 4, 5 are divisible by 5 if digits are not repeated?
Prove the following by the principle of mathematical induction:
$1.3 + 3.5 + 5.7 + ... + (2\text{n} - 1)(2\text{n} + 1)= \frac{\text{n}(4\text{n}^2+6\text{n}-1)}{3}$
→$1.3 + 3.5 + 5.7 + ... + (2\text{n} - 1)(2\text{n} + 1)= \frac{\text{n}(4\text{n}^2+6\text{n}-1)}{3}$