Question

find the maximum and minimum value of 4cosX + 5sinX - 3

Answer 1

The maximum value of :
3|sinx| + 4|cosx| is same as the maximum value of 3sinx +4cosx for x in first quadrant.
3sinx+4cosx
=5(3/5 sinx + 4/5 cosx)
=5sin(x+A).
where 3/5=cosA and 4/5=sinA
Max value=5×1=5.Therefore, maximum value of the the expression is same as expression without modulus, but minimum value is not negative.
The minimum value of |sinx| and |cosx| is zero but not simultaneously .
Since, coefficient of sinx is less than cosx; we may consider zero for cosx to get minimum value of the expression.

Answer 2

Answer:

Step-by-step explanation:

Max value is (a^2+ b^2)^1/2+c hence (4^2+ 5^2)^1/2-3 =√41 -3 and similarly min value is -(a^2+ b^2)^1/2+c

Hence -√41-3