Quandaries
and Queries
name : kris
i am a student
secondary 10-12 or 11th
how to solve the equation
cos 2x = sin x for 0<= x < 360
please solve it
thank you
Hi Kris,
Use the double angle expression for the cosine to get
cos 2x = sin x
cos2(x) - sin2(x) = sin(x)
Then replace cos2(x) by 1 - sin2(x) to get
(1 - sin2(x)) - sin2(x) = sin(x)
which simplifies to
2 sin2(x) + sin(x) - 1 = 0
If you let y = sin(x) then this equation is a quadratic in y which you can solve. This will give you two values for y which then gives you two equations
y = sin(x)
to solve for x.
Penny