Question
Find the trigonometric functions of : 240°
✓
Answer
Angle of measure $240^{\circ}$ :
Let $\mathrm{m} \angle \mathrm{XOA}=240^{\circ}$
Its terminal arm (ray $O A)$ intersects the standard unit circle at $P(x, y)$. Draw seg PM perpendicular to the $X$-axis.
$\triangle O M P$ is a $30^{\circ}-60^{\circ}-90^{\circ}$ triangle.
$O P =1$
$O M =\frac{1}{2} \mathrm{OP}$
$ =\frac{1}{2}(1)$
$ =\frac{1}{2}$
$P M =\frac{\sqrt{3}}{2} \mathrm{OP}$
$ =\frac{\sqrt{3}}{2}(1)$
$ =\frac{\sqrt{3}}{2} $
Since point $P$ lies in the 3 rd quadrant, $x<0, y<0$
$ \therefore \quad x=-\mathrm{OM}=-\frac{1}{2} \text { and } y=-\mathrm{PM}=-\frac{\sqrt{3}}{2}$
$\therefore \quad \mathrm{P} \equiv\left(\frac{-1}{2},-\frac{\sqrt{3}}{2}\right)$
$\sin 240^{\circ}=y=-\frac{\sqrt{3}}{2}$
$\cos 240^{\circ}=x=-\frac{1}{2}$
$\tan 240^{\circ}=\frac{y}{x}=\frac{\left(-\frac{\sqrt{3}}{2}\right)}{\left(-\frac{1}{2}\right)}=\sqrt{3}$
$\operatorname{cosec} 240^{\circ}=\frac{1}{y}=\frac{1}{\left(\frac{-\sqrt{3}}{2}\right)}=-\frac{2}{\sqrt{3}}$
$\sec 240^{\circ}=\frac{1}{x}=\frac{1}{-\frac{1}{2}}=-2$
$\cot 240^{\circ}=\frac{x}{y}=\frac{\left(\frac{-1}{2}\right)}{\left(\frac{-\sqrt{3}}{2}\right)}=\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
$\text{x}^4+4\text{x}^3+6\text{x}^2+4\text{x}+9,$ when $\text{x}=-1+\text{i}\sqrt{2}$
→The sum of first three terms of a G.P. is $\frac{39}{10}$ and their product is 1. Find the common ratio and the terms.
→From 4 officers and 8 jawans in how many ways can 6 be chosen:
-
To include exactly one officer.
-
To include at least one officer?
In any $\triangle \text{ABC},$ if $a^2, b^2, c^2$ are in A.P., prove that $\cot\text{A},\cot\text{B}$ and $\cot\text{C}$ are also in A.P.
→If $S_1, S_2, ..., S_n$ are the sums of n terms of $n$ G.P.'s whose first terms is $1$ in each and common ratio are $1, 2, 3, ..., n$ respectively, then prove that $S_1, + S_2 + 2S_3+ 3S_4 + ... (n - 1) S_n = 1^n + 2^n + 3^n + ... + n^n.$
→Find sum of these numbers in G.P. is $21$ and the sum of their aquares is $189$. Find the numbers.
→A rod of length 12cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with x-axis.
Five cards are drawn from form a pack of 52 cards. what is the chance that these 5 will contain:
- Just one ace
- At least one ace.
Find the number of words formed by permuting all the letters of the following words:
SERIES.
SERIES.
If S, P, R are the sum, product, and sum of the reciprocals of n terms of a G.P, respectively,
→then verify that $\left[\frac{S}{R}\right]^n= P ^2$.