Write the number of points of intersection of the curves 2y = 1 and y

1.	Write the number of points of intersection of the curves 2y = 1 and y = cos x, 0 ≤ x ≤ 2π.
Answer» 2y = 1 i.e. y = \(\frac{1}2\) and y = cos x so, to get the intersection points we must equate both the equations i.e. cos x = \(\frac{1}2\) so, cos x = cos 60° and we know if cos x = cos a then x = 2nπ ± a where a ϵ [0, π] so here x = 2nπ ± \(\frac{π}3\) So the possible values which belong [0,2π] are \(\frac{π}3\)and \(\frac{5π}3\). There are a total of 2 points of intersection.

Write the number of points of intersection of the curves 2y = 1 and y = cos x, 0 ≤ x ≤ 2π.

Answer»

2y = 1

i.e. y = \(\frac{1}2\)

and y = cos x

so, to get the intersection points we must equate both the equations

i.e. cos x = \(\frac{1}2\)

so, cos x = cos 60°

and we know if cos x = cos a

then x = 2nπ ± a where a ϵ [0, π]

so here

x = 2nπ ± \(\frac{π}3\)

So the possible values which belong [0,2π] are \(\frac{π}3\)and \(\frac{5π}3\).

There are a total of 2 points of intersection.