Draw the graph of the function y = 4 + 3 sin x. Find its maximum and minimum values.

Solution : y = 4 + 3 sin x

1) The maximum value of y = 4 + 3 sin x is M = d + a = 4 +3 = 7. Thus maxima attained at x = 45⁰ and 225⁰

2) The minimum value is m = d - a = 4 - 3 = 1. Thus minima attained at x = 135⁰ and 315⁰.

EXAMPLE 3

Draw the graph of  

Solution: The values of x and y are tabulated as

i) The period of   is T = 4p i.e 360 ⁰

ii) Its maximum value M = d + a = 0 + = 0.75
at x = p i.e 180 ⁰

iii) Its minimum value m = d - a = = -0.75
at x = 3p i.e. 540⁰

Fig.24

Index

5. 1 Circular function
5. 2 Periodic function
5. 3 Even & Odd
5.4 Graphs of Trigonometric Functions Supplementary Problems

Chapter 6