Question

At which values in the interval [0, 2π) will the functions f (x) = cos 2x - 5 and g(x) = sin3x - 5 intersect?

A.
x = 0, π/10, π/2, 9π/10, 13π/10

B.
x = 3π/10, π/2, 7π/10, 13π/10, 17π/10

C.
x = π/10, π/2, 9π/10, 13π/10, 17π/10

D.
x = 0, π/2, π/10, 13π/10, 17π/10

Answer 1

Intersection will be when
\[f(x)=g(x)\]
That is
\[\cos2x-5=\sin3x-5\]
\[\cos2x=\sin3x\]
\[\cos2x=\cos(\frac{ \pi }{ 2 }-3x)\]
\[2x=\frac{ \pi }{ 2 }-3x +2k \pi\]
and
\[2x=-\frac{ \pi }{ 2 }+3x+2k \pi \]
Where \[k \in \mathbb{Z}\]
By giving different values to k, you will get the right solution

Answer 2

So what is the answer?

Answer 3

@surjithayer

Answer 4

Set the limits on x to be between 0 and \(2\pi\). That'll give you a range for k, k can take all the integer values in this range.
Plug in those values of k, and that'll give you your x

Answer 5

I don't know how to