7. WMA11/01 Edexcel IAL P1 January 2020, Q7 (Trignimetric Ratios: Transforming Trignometric Graphs)
Figure 3 shows part of the curve C1 with equation y = 3sinx, where x is measured in degrees.
The point P and the point Q lie on C1 and are shown in Figure 3.
(a) State
the coordinates of P,
the coordinates of Q.
(3)
A different curve C2 has equation y = 3 sin x + k, where k is a constant.
The curve C2 has a maximum y value of 10
The point R is the minimum point on C2 with the smallest positive x coordinate.
(b) State the coordinates of R.
(2)
SOLUTION
a- i-
The graph y=3f(x) is vertical stretch of a curve. Moreover, the scale factor is 3. Since the point P is the point on the first maximum point, the x-cordinate is 90, and due to vertical stretch by 3 scale factor, the y-coordinate is 3.
Hence, the point P is
a- ii-
We know that the graph y=3f(x) is a vertical stretch of a curve; therefore, there is no change on the x-coordinates of the point.
Hence, the point P is
b-
The graph of y = 3 sin x + k is a verticaly stretched by a scale factor 3 and vertically translated upwards by k units. Second, it is given that the curve C2has a maximum y-value of 10, which means after the vertical stretch of scale factor=3 and vertical translation of k units, the maximum point y-value is 10.
Keeping this in mind that R is the minimum point on C2 with the smallest positive x coordinate, this means that point R is the first minimum point along the positive x-axis.
Hence, the point R is (270, 4).
