Download App

Trigonometry – I — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – I2 Marks
Question
Find the other trigonometric functions if : $\cot x=\frac{3}{4}$, $x$ lies in the third quadrant.
✓

Answer

$ \text { We have } \cot x=\frac{3}{4}$
$\therefore \operatorname{cosec}^2 x=1+\cot ^2 x$
$=1+\left(\frac{3}{4}\right)^2$
$=1+\frac{9}{16}$
$=\frac{25}{16}$
$\therefore \operatorname{cosec} x= \pm \frac{5}{4}$
But $x$ lies in the third quadrant $\therefore \operatorname{cosec} \mathrm{x}$ is negative
$ \therefore \operatorname{cosec} x=-\frac{5}{4}$
$\therefore \sin \mathrm{x}=\frac{1}{\operatorname{cosec} x}=\frac{1}{\left(-\frac{5}{4}\right)}=-\frac{4}{5}$
Now, $\cot x=\frac{\cos x}{\sin x}=\frac{3}{4}$
$\therefore \cos x=\frac{3}{4} \sin x=\frac{3}{4}\left(-\frac{4}{5}\right)=-\frac{3}{5}$
$\sec x=\frac{1}{\cos x}=\frac{1}{\left(-\frac{3}{5}\right)}=-\frac{5}{3} $
$\tan x=\frac{1}{\cot x}=\frac{1}{\frac{3}{4}}=\frac{4}{3}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Trigonometry – I→Trigonometry – I — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

How many quadratic equations can be formed using numbers from 0, 2, 4, 5 as coefficients if a coefficient can be repeated in an equation?
→
The difference between the two acute angkes of a right angles triangle is $\frac{2\pi}{5}$ redians. Express the angles in degrees.
→
Find the 12th term from the end of the following arithmetic progressions,

3, 8, 13, ..., 253
→
There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?
→
Show that the tangents drawn from the point $(-4,-9)$ to the parabola $y^2=16 x$ are perpendicular to each other.
→
Solve the following system of equations in R.
$\frac{2\text{x}+1}{7\text{x}-1}>5,\frac{\text{x}+7}{\text{x}-8}>2$
→
Find the value of k, if the length of the tangent segment from the point (8, -3) to the circle

$x^2+y^2-2 x+k y-23=0$ is $\sqrt{ } 10$.

→
Express the following in the form of $a + ib, a, b \in R, i = \sqrt{-1}.$ State the values of a and b:
$\frac{i(4+3 i)}{1-i}$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow\infty}\Big(\text{a}^{\frac{1}{\text{x}}}-1\Big)\text{x}$
→
Show that $\tan^2 \theta + \cot^2 \theta \geq 2$ for all $\theta \in R$.
→