Trigonometric Graphs
1. Each of the graphs below has an equation of the form y = asin bx
or y = acos bx. Write down the values of a and b.
(a)
(b)
y
y
3
3
2
2
1
1
180
360
180
x
−1
−1
−2
−2
−3
−3
−4
360 x
−4
(c)
7
6
5
4
3
2
1
y
4
3
2
1
180
−1
−2
−3
−4
−5
−6
−7
−8
(e)
(d)
y
180
360 x
−1
−2
−3
−4
−5
(f)
y
y
4
4
3
3
2
2
1
1
180
−1
360 x
360 x
180
−1
−2
−2
−3
−3
−4
−4
−5
−5
360 x
y
(g)
y
(h)
4
2
3
2
1
1
120
240
360 x
120
240
360 x
−1
−1
−2
−3
−2
−4
−3
−5
(i)
(j)
y
y
4
4
3
3
2
2
1
1
90
−1
x
90
x
−1
−2
−2
−3
−3
−4
−4
−5
−5
(k)
(l)
y
3
2
1
60
−1
−2
−3
−4
y
6
5
4
3
2
1
x
−1
−2
−3
−4
−5
−6
−7
40
x
2. Each graph below is of the form y = asin(x ± b) .
Write down the equation of each graph.
y
(a)
(b)
y
3
3
2
2
1
1
380 x
200
−1
−2
−2
−3
−3
−4
−4
(c)
400 x
220
−1
(d)
y
y
3
3
2
2
1
1
150
330
170
x
−1
−1
−2
−2
−3
−3
−4
−4
350
x
3. Each graph below is of the form y = acos(x ± b).
Write down the equation of each graph..
y
(a)
(b)
y
3
4
2
3
2
1
1
160
−1
−2
340
130
x
−1
−2
−3
−3
−4
−4
−5
310
x
(c)
(d)
y
y
4
2
3
2
1
1
40
400
−1
25
x
385
−1
−2
−3
−2
−4
−3
−5
4. Make sketches of the following graphs for 0° ≤ x° ≤ 360°
(a) y = 6sin x
(b) y = 4cos x
(c) y = 3sin 2x
(d) y = 4sin 4x
(e) y = 2cos 3x
(f) y = 8cos 4x
(g ) y = 2.5cos 3x
(h) y = 1.2sin 5x
(i) y = 4cos(x – 45)
(j) y = 2sin(x – 30)
(k) y = 5cos(x + 20)
(l) y = 3sin(x + 60)
5. (a) Write down the equation of the
graph opposite in the form
y = asin x.
(b) The line y = 2 meets this
graph at the points P and Q.
Find the coordinates of P and Q.
y
3
2
y= 2
P
Q
1
180
−1
−2
−3
−4
360 x
x
6. (a) Write down the equation of the
graph opposite in the form
y = asin x.
(b) The line y = 4 meets this
graph at the points P and Q.
Find the coordinates of P and Q.
7. (a) Write down the equation of the
graph opposite in the form
y = asin x.
y
6
5
4
3
2
1
y=4
P
Q
180
−1
−2
−3
−4
−5
−6
−7
360 x
y
3
2
(b) The line y = -1 meets this
graph at the points P and Q.
Find the coordinates of P and Q.
1
180
−1
y = -1
360 x
Q
P
−2
−3
−4
8. . (a) Write down the equation of the
graph opposite in the form
y = asin x.
y
5
4
3
2
(b) The line y = -4 meets this
graph at the points P and Q.
Find the coordinates of P and Q.
1
180
−1
360 x
−2
−3
−4
−5
−6
y= -4
P
Q
9. . (a) Write down the equation of the
graph opposite in the form
y = acos x.
(b) The line y = 0.5 meets this
graph at the points P and Q.
Find the coordinates of P and Q.
y
2
1
P
y= 0.5
Q
180
360 x
−1
−2
−3
10. (a) Write down the equation of the
graph opposite in the form
y = acos x.
(b) The line y = 2.5 meets this
graph at the points P and Q.
Find the coordinates of P and Q.
y
4
3
y=2.5
Q
P
2
1
180
360 x
−1
−2
−3
−4
−5
11. (a) Write down the equation of the
graph opposite in the form
y = acos x.
(b) The line y = -3.5 meets this
graph at the points P and Q.
Find the coordinates of P and Q.
6
5
4
3
2
1
−1
−2
−3
−4
−5
−6
−7
y
180
P
360 x
Q
y= -3.5