SOLUTION: Hello amazing tutors, can you help me solve this pleasee, thank youuu
(i)Sketch the graph of the curve y = 3 sin x, for −π ≤ x ≤ π
The straight li
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Question 1040749: Hello amazing tutors, can you help me solve this pleasee, thank youuu
(i)Sketch the graph of the curve y = 3 sin x, for −π ≤ x ≤ π
The straight line y = kx, where k is a constant, passes through the maximum point of this curve for −π ≤ x ≤ π .
(ii) Find the value of k in terms of π
(iii) State the coordinates of the other point, apart from the origin, where the line and the curve
intersect
Found 2 solutions by robertb, josmiceli:
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
(i)
(ii) k will just be the slope of the line passing through the origin.
Since the maximum is 3 over the interval, the slope is . Thus . (The coordinates of the maximum are (,3).)
(iii) The other point of intersection would be (,-3), due to symmetry wrt the origin.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The basic facts you need to know about
the sine curve is:
(1) repeats itself every
radians
(2) the maximum value of is
and this maximum occurs every
radians
-----------------------------------------
(i), (ii), and (iii)
You are given the interval −π ≤ x ≤ π
so, the only place where there is a maximum in this
interval is:
------------------------
Your sine function is , the the maximum is
. Now you know the maximum point is at
( pi/2, 3 )
------------------
The straight line must also pass through that
point and also (0,0) since gives you (0,0)
-------------------
The slope, , is , so the equation is:
-------------------
Here are plots of
and
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