CAIE: A Level - Mathematics 9709 - Pure Mathematics 1

Trigonometry / Transformation of Trigonometric Functions

KEYPOINTS:

y = a sin x OR y = a cos x [Vertical Stretch]

If a > 1, the graph is stretched vertically by a factor of a.

If 0 < a < 1, the graph is compressed.

If a < 0, the graph is reflected in the x–axis.

y = sin bx OR y = cos bx [Horizontal Stretch]

If b > 1, the graph is compressed horizontally by a factor of b.

If 0 < b < 1, the graph is stretched.

If b < 0, the graph is reflected in the y–axis.

y = sin (x + c) OR y = cos (x + c) [Horizontal Translation]

for c > 0, the graph is translated c to the left.

for c < 0, the graph is translated c to the right.

y = sin x + d OR y = cos x + d [Vertical Translation]

for d > 0, the graph is translated d up.

for d < 0, graph is translated d down.

Past Papers Topic Wise Questions A Level: Mathematics 9709 - Pure Mathematics 1 Trigonometry | Transformation of Trigonometric Functions

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