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Recent questions tagged trigonometry
0
votes
0
answers
1
ISI2014DCG54
The number of real roots of the equation $1+\cos ^2x+\cos ^3 x – \cos^4x=5$ is equal to $0$ $1$ $3$ $4$
asked
Sep 23
in
Numerical Ability
by
Arjun
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(
424k
points)

25
views
isi2014dcg
numericalability
trigonometry
roots
0
votes
1
answer
2
ISI2015MMA13
The number of real roots of the equation $2 \cos \bigg( \frac{x^2+x}{6} \bigg) = 2^x +2^{x} \text{ is }$ $0$ $1$ $2$ infinitely many
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
424k
points)

12
views
isi2015mma
numericalability
quadraticequations
trigonometry
0
votes
0
answers
3
ISI2015MMA27
Let $\cos ^6 \theta = a_6 \cos 6 \theta + a_5 \cos 5 \theta + a_4 \cos 4 \theta + a_3 \cos 3 \theta + a_2 \cos 2 \theta + a_1 \cos \theta +a_0$. Then $a_0$ is $0$ $1/32$ $15/32$ $10/32$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
424k
points)

12
views
isi2015mma
numericalability
trigonometry
nongate
0
votes
1
answer
4
ISI2015MMA34
If $f(x) = \dfrac{\sqrt{3}\sin x}{2+\cos x}$, then the range of $f(x)$ is the interval $[1, \sqrt{3}/2]$ the interval $[ \sqrt{3}/2, 1]$ the interval $[1, 1]$ none of the above
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

15
views
isi2015mma
calculus
functions
range
trigonometry
nongate
0
votes
0
answers
5
ISI2015MMA35
If $f(x)=x^2$ and $g(x)= x \sin x + \cos x$ then $f$ and $g$ agree at no points $f$ and $g$ agree at exactly one point $f$ and $g$ agree at exactly two points $f$ and $g$ agree at more than two points
asked
Sep 23
in
Geometry
by
Arjun
Veteran
(
424k
points)

14
views
isi2015mma
trigonometry
nongate
0
votes
1
answer
6
ISI2015MMA49
The polar equation $r=a \cos \theta$ represents a spiral a parabola a circle none of the above
asked
Sep 23
in
Geometry
by
Arjun
Veteran
(
424k
points)

10
views
isi2015mma
trigonometry
nongate
0
votes
1
answer
7
ISI2015MMA63
Let $\theta=2\pi/67$. Now consider the matrix $A = \begin{pmatrix} \cos \theta & \sin \theta \\  \sin \theta & \cos \theta \end{pmatrix}$. Then the matrix $A^{2010}$ ... $\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$
asked
Sep 23
in
Linear Algebra
by
Arjun
Veteran
(
424k
points)

11
views
isi2015mma
linearalgebra
matrices
trigonometry
0
votes
0
answers
8
ISI2015MMA64
Let the position of a particle in three dimensional space at time $t$ be $(t, \cos t, \sin t)$. Then the length of the path traversed by the particle between the times $t=0$ and $t=2 \pi$ is $2 \pi$ $2 \sqrt{2 \pi}$ $\sqrt{2 \pi}$ none of the above
asked
Sep 23
in
Geometry
by
Arjun
Veteran
(
424k
points)

6
views
isi2015mma
trigonometry
curves
nongate
0
votes
0
answers
9
ISI2015MMA66
The smallest positive number $K$ for which the inequality $\mid \sin ^2 x – \sin ^2 y \mid \leq K \mid xy \mid$ holds for all $x$ and $y$ is $2$ $1$ $\frac{\pi}{2}$ there is no smallest positive value of $K$; any $K>0$ will make the inequality hold.
asked
Sep 23
in
Others
by
Arjun
Veteran
(
424k
points)

6
views
isi2015mma
inequality
trigonometry
nongate
0
votes
0
answers
10
ISI2015MMA72
The map $f(x) = a_0 \cos \mid x \mid +a_1 \sin \mid x \mid +a_2 \mid x \mid ^3$ is differentiable at $x=0$ if and only if $a_1=0$ and $a_2=0$ $a_0=0$ and $a_1=0$ $a_1=0$ $a_0, a_1, a_2$ can take any real value
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

5
views
isi2015mma
calculus
differentiability
trigonometry
0
votes
1
answer
11
ISI2015MMA86
The coordinates of a moving point $P$ satisfy the equations $\frac{dx}{dt} = \tan x, \:\:\:\: \frac{dy}{dt}=\sin^2x, \:\:\:\:\: t \geq 0.$ If the curve passes through the point $(\pi/2, 0)$ when $t=0$, then the equation of the curve in rectangular coordinates is $y=1/2 \cos ^2 x$ $y=\sin 2x$ $y=\cos 2x+1$ $y=\sin ^2 x1$
asked
Sep 23
in
Geometry
by
Arjun
Veteran
(
424k
points)

12
views
isi2015mma
trigonometry
curves
nongate
0
votes
2
answers
12
ISI2015DCG4
If $\tan x=p+1$ and $\tan y=p1$, then the value of $2 \cot (xy)$ is $2p$ $p^2$ $(p+1)(p1)$ $\frac{2p}{p^21}$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

42
views
isi2015dcg
numericalability
trigonometry
0
votes
0
answers
13
ISI2015DCG40
The equations $x=a \cos \theta + b \sin \theta$ and $y=a \sin \theta + b \cos \theta$, $( 0 \leq \theta \leq 2 \pi$ and $a,b$ are arbitrary constants) represent a circle a parabola an ellipse a hyperbola
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

41
views
isi2015dcg
numericalability
trigonometry
geometry
0
votes
1
answer
14
ISI2015DCG59
If in a $\Delta ABC$, $\angle B = \frac{2 \pi}{3}$, then $\cos A + \cos C$ lies in $[\: \sqrt{3}, \sqrt{3}\:]$ $(\: – \sqrt{3}, \sqrt{3}\:]$ $(\:\frac{3}{2}, \sqrt{3}\:)$ $(\:\frac{3}{2}, \sqrt{3}\:]$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

21
views
isi2015dcg
numericalability
geometry
trigonometry
+1
vote
1
answer
15
ISI2015DCG61
The value of $\sin^6 \frac{\pi}{81} + \cos^6 \frac{\pi}{81}1+3 \sin ^2 \frac{\pi}{81} \cos^2 \frac{\pi}{81}$ is $\tan ^6 \frac{\pi}{81}$ $0$ $1$ None of these
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

16
views
isi2015dcg
numericalability
trigonometry
0
votes
0
answers
16
ISI2015DCG62
The number of values of $x$ for which the equation $\cos x = \sqrt{\sin x} – \dfrac{1}{\sqrt{\sin x}}$ is satisfied, is $1$ $2$ $3$ more than $3$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

11
views
isi2015dcg
numericalability
trigonometry
0
votes
1
answer
17
ISI2015DCG63
If $\sin^{1} \frac{1}{\sqrt{5}}$ and $\cos ^{1} \frac{3}{\sqrt{10}}$ lie in $\bigg[0, \dfrac{\pi}{2}\bigg]$, their sum is equal to $\frac{\pi}{6}$ $\frac{\pi}{3}$ $ \sin^ {1}\frac{1}{\sqrt{50}}$ $\frac{\pi}{4}$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

13
views
isi2015dcg
numericalability
trigonometry
0
votes
2
answers
18
ISI2015DCG64
If $\cos 2 \theta = \sqrt{2}(\cos \theta – \sin \theta)$ then $\tan \theta$ equals $1$ $1$ or $1$ $\frac{1}{\sqrt{2}}, – \frac{1}{\sqrt{2}}$ or $1$ None of these
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

16
views
isi2015dcg
numericalability
trigonometry
+1
vote
1
answer
19
ISI2015DCG65
The value of $\sin ^2 5^{\circ} + \sin ^2 10^{\circ} + \sin ^2 15^{\circ} + \dots + \sin^2 90^{\circ}$ is $8$ $9$ $9.5$ None of these
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

18
views
isi2015dcg
numericalability
trigonometry
0
votes
1
answer
20
ISI2015DCG66
If $\sin(\sin^{1} \frac{2}{5} + \cos ^{1} x) =1$, then $x$ equals $1$ $\frac{2}{5}$ $\frac{3}{5}$ None of these
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

18
views
isi2015dcg
numericalability
trigonometry
0
votes
1
answer
21
ISI2016DCG4
If $f(x)=\begin{bmatrix}\cos\:x & \sin\:x & 0 \\ \sin\:x & \cos\:x & 0 \\ 0 & 0 & 1 \end{bmatrix}$ then the value of $\big(f(x)\big)^2$ is $f(x)$ $f(2x)$ $2f(x)$ None of these
asked
Sep 18
in
Linear Algebra
by
gatecse
Boss
(
16.8k
points)

10
views
isi2016dcg
linearalgebra
matrices
trigonometry
functions
0
votes
2
answers
22
ISI2016DCG5
If $\tan\: x=p+1$ and $\tan\; y=p1,$ then the value of $2\:\cot\:(xy)$ is $2p$ $p^{2}$ $(p+1)(p1)$ $\frac{2p}{p^{2}1}$
asked
Sep 18
in
Geometry
by
gatecse
Boss
(
16.8k
points)

19
views
isi2016dcg
trigonometry
nongate
0
votes
0
answers
23
ISI2016DCG40
The equations $x=a\cos\theta+b\sin\theta$ and $y=a\sin\theta+b\cos\theta,(0\leq\theta\leq2\pi$ and $a,b$ are arbitrary constants$)$ represent a circle a parabola an ellipse a hyperbola
asked
Sep 18
in
Geometry
by
gatecse
Boss
(
16.8k
points)

7
views
isi2016dcg
trigonometry
curves
nongate
0
votes
0
answers
24
ISI2016DCG46
Let $I=\int(\sin\:x\cos\:x)(\sin\:x+\cos\:x)^{3}dx$ and $K$ be a constant of integration. Then the value of $I$ is $(\sin\:x+\cos\:x)^{4}+K$ $(\sin\:x+\cos\:x)^{2}+K$ $\frac{1}{4}(\sin\:x+\cos\:x)^{4}+K$ None of these
asked
Sep 18
in
Calculus
by
gatecse
Boss
(
16.8k
points)

12
views
isi2016dcg
calculus
integration
trigonometry
0
votes
0
answers
25
ISI2016DCG59
If in a $\triangle ABC,\angle B=\dfrac{2\pi}{3},$ then $\cos A+\cos C$ lies in $\left[\:\sqrt{3},\sqrt{3}\:\right]$ $\left(\:\sqrt{3},\sqrt{3}\:\right]$ $\left(\:\frac{3}{2},\sqrt{3}\:\right)$ $\left(\:\frac{3}{2},\sqrt{3}\:\right]$
asked
Sep 18
in
Geometry
by
gatecse
Boss
(
16.8k
points)

3
views
isi2016dcg
geometry
triangles
trigonometry
nongate
0
votes
1
answer
26
ISI2016DCG61
The value of $\sin^{6}\frac{\pi}{81}+\cos^{6}\frac{\pi}{81}1+3\sin^{2}\frac{\pi}{81}\:\cos^{2}\frac{\pi}{81}$ is $\tan^{6}\frac{\pi}{81}$ $0$ $1$ None of these
asked
Sep 18
in
Geometry
by
gatecse
Boss
(
16.8k
points)

11
views
isi2016dcg
trigonometry
nongate
0
votes
0
answers
27
ISI2016DCG62
The number of values of $x$ for which the equation $\cos x=\sqrt{\sin x}\frac{1}{\sqrt{\sin x}}$ is satisfied is $1$ $2$ $3$ more than $3$
asked
Sep 18
in
Geometry
by
gatecse
Boss
(
16.8k
points)

7
views
isi2016dcg
trigonometry
nongate
0
votes
1
answer
28
ISI2016DCG63
If $\sin^{1}\frac{1}{\sqrt{5}}$ and $\cos^{1}\frac{3}{\sqrt{10}}$ lie in $\left[0,\frac{\pi}{2}\right],$ their sum is equal to $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\sin^{1}\frac{1}{\sqrt{50}}$ $\frac{\pi}{4}$
asked
Sep 18
in
Geometry
by
gatecse
Boss
(
16.8k
points)

24
views
isi2016dcg
trigonometry
nongate
0
votes
1
answer
29
ISI2016DCG64
If $\cos2\theta=\sqrt{2}(\cos\theta\sin\theta)$ then $\tan\theta$ equals $1$ $1$ or $1$ $\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}$ or $1$ None of these
asked
Sep 18
in
Geometry
by
gatecse
Boss
(
16.8k
points)

12
views
isi2016dcg
trigonometry
nongate
0
votes
1
answer
30
ISI2016DCG65
The value of $\sin^{2}5^{\circ}+\sin^{2}10^{\circ}+\sin^{2}15^{\circ}+\cdots+\sin^{2}90^{\circ}$ is $8$ $9$ $9.5$ None of these
asked
Sep 18
in
Geometry
by
gatecse
Boss
(
16.8k
points)

10
views
isi2016dcg
trigonometry
summation
nongate
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