Trigonometrical Equations 3 Question 18

19. Find the coordinates of the points of intersection of the curves y=cosx,y=sin3x, if π2xπ2.

(1982, 3M)

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Answer:

Correct Answer: 19. π8,cosπ8π4,cosπ43π8,cos3π8

Solution:

  1. The point of intersection is given by

sin3x=cosx=sinπ2x3x=nπ+(1)nπ2x

(i) Let n be even i.e. n=2m

3x=2mπ+π2xn=mπ2+π8

(ii) Let n be odd i.e. n=(2m+1)

3x=(2m+1)ππ2x3x=2mπ+π2+xx=mπ+π4 Now, π2xπ2x=π8,π43π8 [from Eqs. (i) and (ii)] 

Thus, points of intersection are

π8,cosπ8π4,cosπ43π8,cos3π8



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