The period of the function f( thet...

The period of the function ` f( theta ) = 4 + 4 sin ^3 theta -3 sin theta ` is

`(2 pi)/(3)`

`(pi)/(3)`

`(pi)/(2)`

`pi`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

TRIGONOMETRIC FUNCTIONS
NEW JOYTHI PUBLICATION|Exercise EXERCISE|44 Videos
THREE DIMENSIONAL GEOMETRY
NEW JOYTHI PUBLICATION|Exercise Objective|36 Videos
VECTOR ALGEBRA
NEW JOYTHI PUBLICATION|Exercise CONTINUOUS EVALUATION|2 Videos

Similar Questions

Explore conceptually related problems

If tan theta =-4/3, then sin theta is

The expression cos 3 theta + sin 3 theta + (2 sin 2 theta-3) (sin theta- cos theta) is positive for all theta in

the solution of sin ^3 theta cos theta - sin theta cos^3 theta = 1/4 is

Solve sin 6 theta=sin 4 theta-sin 2 theta .

To find the sum sin^(2) ""(2pi)/(7) + sin^(2)""(4pi)/(7) +sin^(2)""(8pi)/(7) , we follow the following method. Put 7theta = 2npi , where n is any integer. Then " " sin 4 theta = sin( 2npi - 3theta) = - sin 3theta This means that sin theta takes the values 0, pm sin (2pi//7), pmsin(2pi//7), pm sin(4pi//7), and pm sin (8pi//7) . From Eq. (i), we now get " " 2 sin 2 theta cos 2theta = 4 sin^(3) theta - 3 sin theta or 4 sin theta cos theta (1-2 sin^(2) theta)= sin theta ( 4sin ^(2) theta -3) Rejecting the value sin theta =0 , we get " " 4 cos theta (1-2 sin^(2) theta ) = 4 sin ^(2) theta - 3 or 16 cos^(2) theta (1-2 sin^(2) theta)^(2) = ( 4sin ^(2) theta -3)^(2) or 16(1-sin^(2) theta) (1-4 sin^(2) theta + 4 sin ^(4) theta) " " = 16 sin ^(4) theta - 24 sin ^(2) theta +9 or " " 64 sin^(6) theta - 112 sin^(4) theta - 56 sin^(2) theta -7 =0 This is cubic in sin^(2) theta with the roots sin^(2)( 2pi//7), sin^(2) (4pi//7), and sin^(2)(8pi//7) . The sum of these roots is " " sin^(2)""(2pi)/(7) + sin^(2)""(4pi)/(7) + sin ^(2)""(8pi)/(7) = (112)/(64) = (7)/(4) . The value of (tan^(2)""(pi)/(7) + tan^(2)""(2pi)/(7) + tan^(2)""(3pi)/(7))xx (cot^(2)""(pi)/(7) + cot^(2)""(2pi)/(7) + cot^(2)""(3pi)/(7)) is

To find the sum sin^(2) ""(2pi)/(7) + sin^(2)""(4pi)/(7) +sin^(2)""(8pi)/(7) , we follow the following method. Put 7theta = 2npi , where n is any integer. Then " " sin 4 theta = sin( 2npi - 3theta) = - sin 3theta This means that sin theta takes the values 0, pm sin (2pi//7), pmsin(2pi//7), pm sin(4pi//7), and pm sin (8pi//7) . From Eq. (i), we now get " " 2 sin 2 theta cos 2theta = 4 sin^(3) theta - 3 sin theta or 4 sin theta cos theta (1-2 sin^(2) theta)= sin theta ( 4sin ^(2) theta -3) Rejecting the value sin theta =0 , we get " " 4 cos theta (1-2 sin^(2) theta ) = 4 sin ^(2) theta - 3 or 16 cos^(2) theta (1-2 sin^(2) theta)^(2) = ( 4sin ^(2) theta -3)^(2) or 16(1-sin^(2) theta) (1-4 sin^(2) theta + 4 sin ^(4) theta) " " = 16 sin ^(4) theta - 24 sin ^(2) theta +9 or " " 64 sin^(6) theta - 112 sin^(4) theta - 56 sin^(2) theta -7 =0 This is cubic in sin^(2) theta with the roots sin^(2)( 2pi//7), sin^(2) (4pi//7), and sin^(2)(8pi//7) . The sum of these roots is " " sin^(2)""(2pi)/(7) + sin^(2)""(4pi)/(7) + sin ^(2)""(8pi)/(7) = (112)/(64) = (7)/(4) . The value of (tan^(2)""(pi)/(7) + tan^(2)""(2pi)/(7) + tan^(2)""(3pi)/(7))/(cot^(2)""(pi)/(7) + cot^(2)""(2pi)/(7) + cot^(2)""(3pi)/(7)) is

To find the sum sin^(2) ""(2pi)/(7) + sin^(2)""(4pi)/(7) +sin^(2)""(8pi)/(7) , we follow the following method. Put 7theta = 2npi , where n is any integer. Then " " sin 4 theta = sin( 2npi - 3theta) = - sin 3theta This means that sin theta takes the values 0, pm sin (2pi//7), pmsin(2pi//7), pm sin(4pi//7), and pm sin (8pi//7) . From Eq. (i), we now get " " 2 sin 2 theta cos 2theta = 4 sin^(3) theta - 3 sin theta or 4 sin theta cos theta (1-2 sin^(2) theta)= sin theta ( 4sin ^(2) theta -3) Rejecting the value sin theta =0 , we get " " 4 cos theta (1-2 sin^(2) theta ) = 4 sin ^(2) theta - 3 or 16 cos^(2) theta (1-2 sin^(2) theta)^(2) = ( 4sin ^(2) theta -3)^(2) or 16(1-sin^(2) theta) (1-4 sin^(2) theta + 4 sin ^(4) theta) " " = 16 sin ^(4) theta - 24 sin ^(2) theta +9 or " " 64 sin^(6) theta - 112 sin^(4) theta - 56 sin^(2) theta -7 =0 This is cubic in sin^(2) theta with the roots sin^(2)( 2pi//7), sin^(2) (4pi//7), and sin^(2)(8pi//7) . The sum of these roots is " " sin^(2)""(2pi)/(7) + sin^(2)""(4pi)/(7) + sin ^(2)""(8pi)/(7) = (112)/(64) = (7)/(4) . The value of tan^(2)""(pi)/(7)tan ^(2)""(2pi)/(7) tan ^(2)""(3pi)/(7) is

if a=cos theta + i sin theta , b=cos 2 theta- i sin 2 theta , c= cos 3theta + i sin 3theta and if |{:(a,,b,,c),(b,,c,,a),(c,,a,,b):}| =0 then

Simplify : sin theta (cosec theta - sin theta)

NEW JOYTHI PUBLICATION-TRIGONOMETRIC FUNCTIONS-QUESTIONS FROM COMPETITIVE EXAMS

The number of solution of cos 2 theta = sin theta in (0, 2 pi) ...
Text Solution
|
the value of tan 40^@ + tan 20^@ + sqrt(3) tan 20^@ tan 40^@ is...
Text Solution
|
The period of the function f( theta ) = 4 + 4 sin ^3 theta -3 ...
Text Solution
|
The value of x in ( 0, pi/2) satisfying the equation sin x cos ...
Text Solution
|
The period of the function f(x) = | sin 2x | + | cos 8x | is
Text Solution
|
the value of cos 20^@ + cos 100^@ + cos 140 ^@ is equal to
Text Solution
|
if (-pi)/(2) lt theta lt pi/2 andn theta ne 0 pi/4 , then valu...
Text Solution
|
If sin theta = 3 sin ( theta + 2 alpha), then the value of ...
Text Solution
|
If alpha , beta , gamma in [0,pi] and if alpha , beta , gamma ...
Text Solution
|
the value of 1/8 (3-4 cos 2 theta + cos 4 theta ) is
Text Solution
|
IF 8 cos 2 theta + 8 sec 2 theta = 65 , 0 lt (pi)/(2) , then ...
Text Solution
|
The value of sqrt(2) (cos 15^@ - sin 15^@ ) is equal to
Text Solution
|
if cos x=-4/5 , where x in [ 0,pi] then the value of cos (x/2)...
Text Solution
|
the value of sec^2 theta + cosec^2 theta is equal to
Text Solution
|
if x in ((pi)/(2),pi) , then ( sec x-1)/( sec x+1) is equal to
Text Solution
|
the value of sec ""(2pi)/(3) + cosec "" ( 5 pi)/(6) is equal to
Text Solution
|
If ( sin x ) /( cos x) xx ( sec x )/( cosec x ) xx ( tan x )/...
Text Solution
|
One of the principal solutions of sqrt(3) sec x=-2 is equal ...
Text Solution
|
if cos alpha + sin alpha = 3/4, then sin ^6 alpha + cos ^6 alp...
Text Solution
|
If cos x + cos^2 x=1 , then the value of sin ^4 x + sin ^6 x ...
Text Solution
|