Home
Class 12
MATHS
Find the range of 12sintheta-9sin^2theta...

Find the range of `12sintheta-9sin^2theta`

Text Solution

Verified by Experts

The correct Answer is:
[-21, 4]
`f(x)=12sintheta-9sin^2theta`
`=-(9sin^2theta-12sintheta)`
`=-(9sin^2theta-12sintheta+4-4)`
`=-((3sintheta-2)^2-4)=4-(3sintheta-2)^2`
Minimum value of `f(theta)` occurs when `(3sintheta-2)^2` is minimum, which is 0.
Hence, range of `f(theta)` is `[4-25,4]-=[-21,4]`.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.6|1 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.7|1 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.4|4 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|2 Videos

Similar Questions

Explore conceptually related problems

if f(theta)=acostheta+bsintheta then -sqrt(a^2+b^2)lef(theta)lesqrt(a^2+b^2) The maximum value of 12sintheta-9sin^2theta is

If 2 sin theta cos theta = 1 , then find the value of sin theta-cos theta .

If 0^(@)angletheta angle20^(@) , then find the value of theta when sin^(2)5theta-sin5theta=0 .

If sin theta+cos theta = 7/5 then sin theta cost theta = 12/25 , find the value of sin theta and cos theta .

The general values of theta satisfying the equation 2sin^2theta-3sintheta-2=0 is (n in Z)dot

If sintheta-costheta=1, then the value of sin^3theta-cos^3theta is __________

If sintheta-costheta=3^(1/2) , then the value of sin^3theta-cos^3theta is __________ .

Find (dy)/(dx) if x= 2 cos theta - cos 2theta and y= 2sin theta - sin 2theta.

Find (dy)/(dx) if x=cos theta - cos 2 theta and" "y = sin theta - sin 2theta