A short tour of Trigonometric graphs |
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We begin with the curve of
y = sin x. You may begin with other trigonometric curve. The curve has a period of 360°, that is, it repeats
itself after 360°.
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The curve
y = sin 2x has the same
shape as y = sin x. It has a
period of 180°. The curve y =
sin x (in red) is compressed to form the curve y = sin 2x (in blue). What do you think of the shape of the curve y = sin 3x? What is its period?
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The curve y = sin (x/2) is formed by elongating the curve y = sin x. Period now is 720°.
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The amplitude of the curve y = 2 sin x is doubled as compared with the original sine curve.
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The curve y =
sin (x - 30°) is formed by
moving y = sin x to the right
by 30°. Similarly, the curve y = sin (x + 30°) is formed by moving y = sin x to the left by 30°.
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The curve y = 1 + sin x is formed by moving y = sin x up by 1 unit. The curve y = -1 + sin x is formed by moving y = sin x down by 1 unit.
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Exercise
The above is the
curve y = 1 + 1.5 sin (2x - 45°) (1) What are the steps of
getting this curve? (2) What is the amplitude of
the curve? and its period? (3) Do you think that the
curve passes through the origin? |
