graph transformations
f(x) ≡ a + b sin x° + c cos x°, x ∈ , 0 ≤ x ≤ 360,
The curve has turning points with coordinates (60, 5) and (240, 1) as shown.
a) State, with a reason, the value of the constant a.
b) Find the values of k and α, where k > 0 and 0 < α < 90, such that
f(x) = a + k sin (x + α)°.
c) Hence, or otherwise, find the exact values of the constants b and c.
I am clueless on all of them.
a) First i assumed the that a =4 because of translation up by 4. usually sin/cos curves have a max of 1.
b) i used the minimum points and maximum points to construct two simultaneous equations:
and minused leaving me with:
ksin(60+α)-ksin(240-α) =4
c) can't do this if i can't do a) or b).
The curve has turning points with coordinates (60, 5) and (240, 1) as shown.
a) State, with a reason, the value of the constant a.
b) Find the values of k and α, where k > 0 and 0 < α < 90, such that
f(x) = a + k sin (x + α)°.
c) Hence, or otherwise, find the exact values of the constants b and c.
I am clueless on all of them.
a) First i assumed the that a =4 because of translation up by 4. usually sin/cos curves have a max of 1.
b) i used the minimum points and maximum points to construct two simultaneous equations:
and minused leaving me with:
ksin(60+α)-ksin(240-α) =4
c) can't do this if i can't do a) or b).
(edited 12 years ago)
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