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

Algebra ->  Length-and-distance -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
(i) graph%28+300%2C+200%2C+-pi%2C+pi%2C+-4%2C+4%2C+3sin%28x%29%2C+%286%2Fpi%29x%29

(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 m+=+%283-0%29%2F%28pi%2F2-0%29+=+6%2Fpi. Thus k+=+6%2Fpi. (The coordinates of the maximum are (pi%2F2,3).)

(iii) The other point of intersection would be (-pi%2F2,-3), due to symmetry wrt the origin.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The basic facts you need to know about
the sine curve is:
(1) +sin%28x%29+ repeats itself every +2pi+
radians
(2) the maximum value of +sin%28x%29+ is +1+
and this maximum occurs every +pi%2F2+%2B-+2pi+
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: +x+=+pi%2F2+
------------------------
Your sine function is +3%2Asin%28+x+%29+, the the maximum is
+3%2A1+=+3+. Now you know the maximum point is at
( pi/2, 3 )
------------------
The straight line +y+=+k%2Ax+ must also pass through that
point and also (0,0) since +y+=+k%2A0+ gives you (0,0)
-------------------
The slope, +k+, is +%28+3+-+0+%29+%2F+%28+pi%2F2+-+0+%29+=+6%2Fpi+, so the equation is:
+y+=+%28+6%2Fpi%29%2Ax+
-------------------
Here are plots of
+y+=+3%2Asin%28x%29+ and
+y+=+%28+6%2Fpi+%29%2Ax+
+graph%28+400%2C+800%2C+-pi%2C+pi%2C+-4%2C+4%2C+3%2Asin%28x%29+%2C+%286%2Fpi%29%2Ax+%29+