English

State whether the following equation has a solution or not? 2sinθ = 3 - Mathematics and Statistics

Advertisements
Advertisements

Question

State whether the following equation has a solution or not?

2sinθ = 3

Sum

Solution

2sinθ = 3

∴ sinθ = `(3)/(2)`

This is not possible because – 1 ≤ sinθ ≤ 1 for any θ.

∴ 2 sinθ = 3 does not have any solution.

shaalaa.com
Trigonometric Equations and Their Solutions
  Is there an error in this question or solution?
Chapter 3: Trigonometric Functions - Exercise 3.1 [Page 75]

RELATED QUESTIONS

Find the principal solution of the following equation: 

cosθ = `(1)/(2)`


Find the principal solution of the following equation :

cot θ = `sqrt(3)`


Find the principal solution of the following equation: 

tan θ = – 1


Find the general solution of the following equation :

cosθ = `sqrt(3)/(2)`


Find the general solution of the following equation:

sec θ = `sqrt(2)`.


Find the general solution of the following equation: 

tan3θ = 3 tanθ.


State whether the following equation have solution or not?

3 tanθ = 5


Select the correct option from the given alternatives:

The principal solutions of equation cot θ = `sqrt3` are ______.


Select the correct option from the given alternatives:

If polar coordinates of a point are `(2, pi/4)`, then its cartesian coordinates are


Select the correct option from the given alternatives:

In ΔABC if c2 + a2 – b2 = ac, then ∠B = ____.


Select the correct option from the given alternatives:

`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____


Select the correct option from the given alternatives:

The principal value branch of sec-1x is


`"cos"["tan"^-1 1/3 + "tan"^-1 1/2]` = ______


If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is ______.


Select the correct option from the given alternatives:

In any ΔABC, if acos B = bcos A, then the triangle is


Find the principal solutions of the following equation:

cot θ = 0


Find the general solutions of the following equation:

`tan^2 theta = 3`


With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`


If 2 tan-1(cos x) = tan-1(2 cosec x), then find the value of x.


If tan-12x + tan-13x = `pi/4`, then find the value of x.


Show that `tan^-1  1/2 - tan^-1  1/4 = tan^-1  2/9`.


Show that `cot^-1  1/3 - tan^-1  1/3 = cot^-1  3/4`.


If cos-1 x + cos-1y + cos-1z = 3π, then show that x2 + y2 + z2 + 2xyz = 1.


Find the principal solutions of sin x − 1 = 0


Find the principal solutions of sin x = `-1/2`


Find the principal solutions of tan x = `-sqrt(3)`


If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1


The value of tan 57°- tan 12°- tan 57° tan 12° is ______.


If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?


The general solution of sec θ = `sqrt2` is


The principal solutions of cot x = `sqrt3` are ______.


The value of `tan^-1  1/3 + tan^-1  1/5 + tan^-1  1/7 + tan^-1  1/8` is ______.


If 4 sin-1x + 6 cos-1 x = 3π then x = ______.


The general solution of sin 2x = cos 2x is ______ 


The general solution of the equation tan θ tan 2θ = 1 is given by ______ 


Which of the following is true in a triangle ABC?


If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.


The general solution of 4sin2 x = 1 is ______.


The general solution of x(1 + y2)1/2 dx + y(1 + x2)1/2 dy = 0 is ______.


The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ is ______.


If a = sin θ + cos θ, b = sin3 θ + cos3 θ, then ______.


Find the general solution of sin θ + sin 3θ + sin 5θ = 0


If tan θ + sec θ = `sqrt(3)`, find the general value of θ.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×