Trigonometric graphs

Question 1

What are the three graphs for trig functions?

Answer 1

the graphs of the trig functions, y = sinx°, y = cosx° and y = tanx°.

Question 2

When referring to trig graphs what is meant by the maximum?

Answer 2

How high the graphs goes.

Question 3

When referring to trig graphs what is meant by the minimum?

Answer 3

How low the graph go’s.

Question 4

What is the amplitude for the trig graph?

Answer 4

If you halve the “vertical distance” between the maximum and minimum values, this is referred to as the amplitude of the graph.

Question 5

What is the period for the trig graphs?

Answer 5

The “horizontal distance” between points on the graph where the pattern repeats itself is called the period of the graph.

Question 6

What is being changed in y =asinx°?

Answer 6

y =asinx° is a change in amplitude.

Question 7

What is being changed in y =sinax°?

Answer 7

y =sinax° is a change in periodicity.

Question 8

What are the steps you should take when sketching any sine or cosine graph?

Answer 8

Step 1: draw the axes first.
Step 2: Then draw the sine, (or cosine),shaped graph.
Step 3: finally fill in the scales on the axes.

Question 9

When is a tangent graph undefined?

Answer 9

At 90°, we say the tangent is undefined (it is too large a number to find - infinity !)

Question 10

What is the usual period of a tangent graph?

Answer 10

180°

Question 11

What is the usual period of a sin and cosine graph?

Answer 11

360°

Question 12

What is meant by -3sinx°?

Answer 12

the graph will flip upside down so the sin line at 90 degrees will be at -3.

Question 13

What is meant by y = sin2x°?

Answer 13

the graph is identical in shape to that of y = sinx°.
its maximum and minimum values are still +1 and –1, and its amplitude is still 1.
its period is no longer 360° – its period is now 360° ÷ 2 = 180°.

Question 14

How do we draw Sine and Cosine Functions (y = asinx°+ b and y = acosx° + b).

Answer 14

When the sine or cosine function has a number added on (or subtracted), the simple effect is to “slide”
the basic sine or cosine function upwards (or downwards) by that amount.
The period of the new function with the added (or subtracted) term remains the same.
The amplitude stays the same. (Half the difference between the highest and lowest points).
But the maximum and the minimum values change.
To draw y = sinx + 2, simply sketch the graph of y = sinx and move each point up by 2.