If = - 3 5 , where < < 3 2 , then 1 2 = - Vidyadip

MCQ

If $\sin \alpha = \frac{{ - 3}}{5},$ where $\pi < \alpha < \frac{{3\pi }}{2},$ then $\cos \frac{1}{2}\alpha = $

✓
$\frac{{ - 1}}{{\sqrt {10} }}$
B
$\frac{1}{{\sqrt {10} }}$
C
$\frac{3}{{\sqrt {10} }}$
D
$\frac{{ - 3}}{{\sqrt {10} }}$

✓

Answer

Correct option: A.

$\frac{{ - 1}}{{\sqrt {10} }}$

a
(a) $\cos (\alpha /2) = - \sqrt {\frac{{1 + \cos \alpha }}{2}} $

$\cos \alpha = - \sqrt {1 - {{\sin }^2}\alpha } $ [$\because \alpha$ lies in $III^{rd}$ Quadrant]

$ = - \sqrt {1 - \frac{9}{{25}}} = - \frac{4}{5}$

$\therefore \,\,\,\cos (\alpha /2) = - \sqrt {\frac{{1 - \frac{4}{5}}}{2}} = - \frac{1}{{\sqrt {10} }}$.

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 "MCQ" from 3. trignometrical ratios,functions and identities→3. trignometrical ratios,functions and identities — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Number of integral points interior to the circle $x^2 + y^2 = 10$ from which exactly one real tangent can be drawn to the curve $\sqrt {{{\left( {x + 5\sqrt 2 } \right)}^2} + {y^2}} \, - \sqrt {{{\left( {x - 5\sqrt 2 } \right)}^2} + {y^2}\,} \, = 10$ are (where integral point $(x, y)$ means $x, y \in I)$

Let S = {1, 2, 3,.....40} and let A be a subset of S such that no two elements in A have their sum divisible by 5 What is the maximum number of elements possible in A?

The product of three geometric means between $4$ and $\frac{1}{4}$ will be

The roots of the equation ${x^4} - 4{x^3} + 6{x^2} - 4x + 1 = 0$ are

Let $S_n=\sum_{k=1}^{4 n}(-1)^{\frac{k(k+1)}{2}} k^2$. Then $S_n$ can take value $(s)$

$(A)$ $1056$ $(B)$ $1088$ $(C)$ $1120$ $(D)$ $1332$

The area of an equilateral triangle inscribed in the circle $x^2 + y^2 - 6x - 8y - 25 = 0$ is:

Let $S_n$ denote the sum of the first $n$ terms of an arithmetic progression. If $\mathrm{S}_{10}=390$ and the ratio of the tenth and the fifth terms is $15: 7$, then $S_{15}-S_5$ is equal to:

Let $P$ be a closed polygon with $10$ sides and $10$ vertices (assume that the sides do not intersect except at the vertices). Let $k$ be the number of interior angles of $P$ that are greater than $180^{\circ}$. The maximum possible value of $k$ is

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals

The centre and radius of the circle $2{x^2} + 2{y^2} - x = 0$ are