Question

Find the periods of the following functions :
(i) sin 2x
(ii) cos 3x
(ii) tan 2x.
​

Answer 1

Answer:

sin2x= 4x

cos3x= 15x

tan2x= 30x

Answer 2

Answer:-

(i) Period of sin 2x = $\pi$

(ii) Period of cos 3x = $\dfrac{2 \pi}{3}$

(iii) Period of tan 2x = $\dfrac{ \pi}{2}$

Explqnation:-

Given

Functions are

(i) sin 2x

(ii) cos 3x

(iii) tan 2x

To Find

Period of the given functions

Solution

(i) sin 2x

Coefficient of x = 2

We know,

$\orange{\mathsf{Period \: of \: tan x}} =\blue{ π}$

Now

Period of sin 2x = $\star \pink{\boxed{\bold{\dfrac{Period \: of \: sinx }{coefficient \: of \: x }}}}$

Period of sin 2x = $\dfrac{2 \pi}{2}$

Period of sin 2x = $\pi$

(ii) cos 3x

Coefficient of x = 3

We know,

$\purple{\mathsf{Period \: of \: tan x}} =\pink{ π}$

Now

Period of cos 3x = $\star \green{\boxed{\bold{\dfrac{Period \: of \: cos x }{coefficient \: of \: x }}}}$

Period of cos 3x = $\dfrac{2 \pi}{3}$

(iii) tan 2x

Coefficient of x = 2

We know,

$\green{\mathsf{Period \: of \: tan x}} =\red{ π}$

Now,

Period of tan 2x = $\star \red{\boxed{\bold{\dfrac{Period \: of \: tan x }{coefficient \: of \: x }}}}$

Period of tan 2x = $\dfrac{ \pi}{2}$