Home
Class 12
MATHS
Solve x^(2) lt "sin" pi/2 x....

Solve `x^(2) lt "sin" pi/2 x`.

Text Solution

Verified by Experts

We have `x^(2) lt "sin" pi/2 x`
Function `y="sin"pi/2x` has period `(2pi)/(pi//2)=4`
Graphs of `y=x^(2)` and `y="sin" pi/2 x` are as shown in the following figure.

Graphs of the functions intersect at two points (0, 0) and (1, 1)
From the figure, `x^(2) lt "sin" pi/2 x` for `x in (0, 1)`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.1|12 Videos
  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.2|6 Videos
  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|34 Videos
  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

For x in (0,(pi)/(2)) prove that "sin"^(2) x lt x^(2) lt " tan"^(2) x

Solve sin^(-1)x + sin^(-1) 2x = (pi)/(3)

Solve: cos 2x gt | sin x| x in [-pi,pi] .

Solve: sin^(-1)x + sin^(-1)2x = pi/3 .

Solve |sin 3x + sinx | + |sin 3x - sinx |= sqrt3, - (pi)/(2) lt x lt (pi)/(2).

Solve sin^(-1) [sin((2x^(2) + 4)/(1 + x^(2)))] lt pi -3

If f(x)={:{((sin 2x)/(sqrt(1-cos 2x))", for " 0 lt x lt pi/2),((cos x)/(pi-2x)", for " pi/2 lt x lt pi):} , then

Solve for x:log_(2)(sin""(x)/(2))lt-1

solve: sin ^ (- 1) x + sin ^ (- 1) 2x = (pi) / (3)

If y = log (sin (x^(2))), 0 lt x lt (pi)/(2), "then " (dy)/(dx) "at x " = (sqrt(pi))/(2) is