MATH 2 STRATEGY: MAKE A MENTAL PICTURE OF THE GRAPHS OF Y = SIN X, Y = COS X, AND Y =
TAN X
Fix in your mind images of the sine, cosine, and tangent graphs, and you’ll find that graphing
trigonometric functions in general is easy and makes sense.Many graphs of trigonometric functions can be variations on these.
The graph in Example 4, for instance, looks a lot like the cosine curve—it has a crest on the y-axis—
but its maximum and minimum are ±2, and it falls to cross the x-axis at and bottoms out at
AMPLITUDE AND PERIOD
For functions in the form y = a sin bx or y = a cos bx, the amplitude of the curve is a, and the
period of the curve is degrees or radians.In other words, it’s the cosine curve with twice the amplitude and half the period. The amplitude is
affected by the number in front of the “cos.” Twice the amplitude means that number is 2. The
period is affected by the number in front of the x. Half the period means the coefficient of x is 2. So
the equation is y = 2 cos 2x. And the answer is (E).
Of course, you can always do a question like Example 4 by picking a point or two. The point (0,2)
satisfies equations (D) and (E) only.
Of those choices, (E) is the only one that works with the point