Question

6(a) Copy and complete the following table of values for the function y=3sin2x for 0<=x<=150 deg (values at x=0,15,30,45,60,75,90,105,120,135,150 deg). (b) Using a scale of 2cm to represent 15 deg on the x-axis and 4cm to represent 1 unit on the y-axis, draw the graph of y=3sin2x for 0<=x<=150 deg. (c) Using your graph, find, correct to one decimal place, the truth set of: (i) 3sin2x+2=0; (ii) (3/2)sin2x=0.25.

Accepted Answer

(a) Table of values for y=3sin2x: at x=0 deg,y=0; x=15 deg,y=1.5; x=30 deg,y=2.6; x=45 deg,y=3.0; x=60 deg,y=2.6; x=75 deg,y=1.5; x=90 deg,y=0; x=105 deg,y=-1.5; x=120 deg,y=-2.6; x=135 deg,y=-3.0; x=150 deg,y=-2.6.
(b) [Graph plotted using the table of values above, on axes scaled 2cm:15deg (x) and 4cm:1 unit (y), forming a sine curve rising to a peak of 3 near x=45deg, crossing zero at x=90deg, and falling to a trough near x=135deg.]
(c) (i) For 3sin2x+2=0, i.e. sin2x=-2/3, so y=-2. Reading from the graph where the curve y=3sin2x equals -2, the truth set is approximately {x: x=111.5 deg or x=148.5 deg} (values read from the graph). (ii) For (3/2)sin2x=0.25, i.e. 3sin2x=0.5, reading where the curve equals 0.5 on the graph gives the truth set {x: x approx 4.8 deg or x approx 85.2 deg}.

WAEC Mathematics 2020 Theory — Question 6

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