SME
Grade 11 Math · Problem type
The equation from the graph’s features
Use this for “Write a cosine with amplitude 4, period π/2 and midline y = −1.”
Chart
Midline y = −1
Amplitude 4
Period π/2 ≈ 1.5708
f(0) = 3
This is an example. Type your own values to start a new problem.
y
=
A
cos(
b
x)
+
(
k
)
P
Period
example
x
Input (radians)
example
y
Output
worked out (not typed)
Formulas
b
=
2π
P
4
=
2π
π
2
y
=
A
×
cos(
b
×
x
)
+
k
3 = 4 × cos(4 × 0) + (−1)
Assumptions
•
y = A cos(bx) + k starts a cycle at its top when x = 0.
•
The period P is 2π ÷ b, so b = 2π ÷ P.
•
A is the height above the midline y = k.
Step-by-step
WE KNOW
A = 4, P = π/2, k = −1, x = 0
FIND
cycles in 2π (b), output (y)
Step 1 · Find cycles in 2π (b)
Use b = 2π ÷ P
One
turn,
2π,
holds
b
periods.
b
=
2π
π
2
The
equation:
y
=
4
cos(
4
x
)
−
1
b
=
4
Step 2 · Find output (y)
Use y = A × cos(b × x) + k
Check
a
point:
multiply
x
by
b
,
take
the
cosine,
stretch
by
A
and
add
k
.
y
=
4
×
cos(4
×
0)
−
1
y
=
4
×
cos(0)
−
1
y
=
4
−
1
y
=
3
Check
Put the numbers back in. Both sides should match.
4
=
2π
π
2
✓
3 = 4 × cos(4 × 0) − 1 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.