मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

State whether the following equation has a solution or not? 3 sin θ = 5

Advertisements
Advertisements

प्रश्न

State whether the following equation has a solution or not?

3 sin θ = 5

बेरीज
Advertisements

उत्तर

3 sin θ = 5

Dividing both sides by 3: `sintheta = 5/3`

The value of sin⁡θ always lies between −1 and +1 for real angles.

But here, sin⁡θ = `5/3` ≈ 1.666, which is greater than 1.

Since sin⁡θ cannot be greater than 1

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Trigonometric Functions - Miscellaneous exercise 3 [पृष्ठ १०९]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 3 Trigonometric Functions
Miscellaneous exercise 3 | Q 3.4 | पृष्ठ १०९

संबंधित प्रश्‍न

Find the principal solution of the following equation:

cot θ = 0


Find the general solution of the following equation:

tan θ = `(1)/(sqrt(3))`


Find the general solution of the following equation:

sec θ = `sqrt(2)`.


Find the general solution of the following equation:

cosec θ = - √2.


Find the general solution of the following equation:

tan θ = - 1


Find the general solution of the following equation:

4 cos2 θ  = 3


Find the general solution of the following equation:

cos 4θ = cos 2θ


In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.


In ΔABC, prove that `sin(("B" − "C")/2) = (("b" − "c")/"a")cos  "A"/(2)`.


In Δ ABC, prove that a3 sin(B – C) + b3sin(C – A) + c3sin(A – B) = 0


With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c2 .


Select the correct option from the given alternatives:

The principal solutions of equation sin θ = `- 1/2` are ______.


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 Δ ABC if ∠A = 45°, ∠B = 30°, then the ratio of its sides are


Select the correct option from the given alternatives:

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


`"cos"^-1 ("cos" (7pi)/6)` = _________.


Select the correct option from the given alternatives:

The value of cot (tan-12x + cot-12x) is


Select the correct option from the given alternatives:

If tan-1(2x) + tan-1(3x) = `pi/4`, then x = _____


Select the correct option from the given alternatives:

`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______


The principal value branch of sec-1x is ______.


Find the general solutions of the following equation:

`tan^2 theta = 3`


Find the general solutions of the following equation:

sin2 θ - cos2 θ = 1


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


In ΔABC, prove that `("a - b")^2 cos^2  "C"/2 + ("a + b")^2 sin^2  "C"/2 = "c"^2`


Prove the following:

`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0


If | x | < 1, then prove that

`2 tan^-1 "x" = tan^-1 ("2x"/(1 - "x"^2)) = sin^-1 ("2x"/(1 + "x"^2)) = cos^-1 ((1 - "x"^2)/(1 + "x"^2))`


Find the principal solutions of cosec x = 2


If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?


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


If function

f(x) = `x - |x|/x, x < 0`
      = `x + |x|/x, x > 0`
      = 1, x = 0, then


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


If sin θ + cos θ = 1, then the general value of θ is ______.


The general value of θ in the equation `2sqrt(3) cos theta = tan theta` is ______.


The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval `[pi/2, (3pi)/2]` is ______.


If y = `(2sinα)/(1 + cosα + sinα)`, then value of `(1 - cos α + sin α)/(1 + sin α)` is ______.


General solution of the equation sin 2x – sin 4x + sin 6x = 0 is ______.


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


The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.


With usual notations, in any ΔABC, if a cos B = b cos A, then the triangle is ______.


If `2sin^-1  3/7` = cos–1β, then find the value of β.


If `sin^-1  4/5 + cos^-1  12/13` = sin–1α, then find the value of α.


If tan3θ = cotθ, then θ =


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×