Question
Find the trigonometric functions of $: -150^\circ$
✓
Answer
Angle of measure $\left(-150^{\circ}\right)$ :
Let $m \angle X O A=-150^{\circ}$
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.
$O P=1 =\frac{\sqrt{3}}{2} \mathrm{OP}$
$ =\frac{\sqrt{3}}{2}(1)$
$ =\frac{\sqrt{3}}{2}$
$\mathrm{PM} =\frac{1}{2} \mathrm{OP}$
$ =\frac{1}{2}(1)=\frac{1}{2} $
Since point $\mathrm{P}$ lies in the $3^{\text {rd }}$ quadrant,
$x<0, y<0$
$\therefore \quad x=-\mathrm{OM}=-\frac{\sqrt{3}}{2} \text { and } y=-\mathrm{PM}=-\frac{1}{2}$
$\therefore \quad \mathrm{P} \equiv\left(-\frac{\sqrt{3}}{2}, \frac{-1}{2}\right)$
$ \sin \left(-150^{\circ}\right)=y=-\frac{1}{2}$
$\cos \left(-150^{\circ}\right)=x=\frac{-\sqrt{3}}{2}$
$\tan \left(-150^{\circ}\right)=\frac{y}{x}=\frac{-\frac{1}{2}}{\frac{-\sqrt{3}}{2}}=\frac{1}{\sqrt{3}} $
$ \sec \left(-150^{\circ}\right)=\frac{1}{x}=\frac{1}{\left(\frac{-\sqrt{3}}{2}\right)}=-\frac{2}{\sqrt{3}}$
$\cot \left(-150^{\circ}\right)=\frac{x}{y}=\frac{\frac{-\sqrt{3}}{2}}{-\frac{1}{2}}=\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
Discuss the continuity and differentiability of :
f(x) = x |x| at x = 0
Find the equation of tangent to the parabola : $y^2=12 x$ from the point $(2,5)$
→Let $f: R \rightarrow R$ be given by $f(x)=x+5$ for all $x \in R$. Draw its graph.
→Find the distance of the line $4x – y = 0$ from the point $P(4, 1)$ measured along the line making an angle of $135^\circ$ with the positive $X-$ axis.
→Show the following quadratic equation:
$ix^2 - x + 12i = 0$
→$ix^2 - x + 12i = 0$
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow3}\big(\text{x}^2-9\big)\Big(\frac{1}{\text{x}+3}-\frac{1}{\text{x}-3}\Big)$
→$\lim\limits_{\text{x}\rightarrow3}\big(\text{x}^2-9\big)\Big(\frac{1}{\text{x}+3}-\frac{1}{\text{x}-3}\Big)$
Evaluate the following limits:
$\lim _{x \rightarrow \infty}\left[\frac{(2 x+1)^2(7 x-3)^3}{(5 x+2)^5}\right]$
→$\lim _{x \rightarrow \infty}\left[\frac{(2 x+1)^2(7 x-3)^3}{(5 x+2)^5}\right]$
$\sin 18^{\circ}=\frac{\sqrt{5}-1}{4}$
→Find the equation of a line which is equidistant from the lines x = -2 and x = 6.
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?