(a) Copy and complete the table for the relation: for .
x
0°
30°
60°
90°
120°
150°
180°
210°
y
2.00
3.23
1.60
-3.23
(b) Using a scale of 2 cm to 60° on the x- axis and 2 cm to one unit on the y- axis, draw the graph of for . (c) From the graph, find the : (i) maximum value of y, correct to two decimal places ; (ii) solution of the equation .
Explanation
(a)
x
0°
30°
60°
90°
120°
150°
180°
210°
y
2.00
3.23
3.60
3.00
1.60
-0.23
-2.00
-3.23
(b) Scale : 2 cm to 60° on the x- axis 2 cm to 2 units on y- axis.
(c)(i) Maximum value of y is 3.60. (ii) Graph : Equation : i.e. (2) - (1) : We draw the line y = 2.5 and find the x- values at the points of intersection of graph with y = 2.5. x = 12° and 102°.