Question

The value 5pi/2 is a solution for the equation 2 sin^2 x- sin x - 1 = 0.

True or False?

Please explain. Thank you!

Answer 1

what's the value of \(\bf sin\left(\frac{5\pi}{2}\right)\) anyway?

Answer 2

@jdoe0001 1

Answer 3

yeap
thus \(\bf 2sin^2(x)-sin(x)-1\implies 2[sin(x)]^2-sin(x)-1
\\ \quad \\
2\left[sin\left(\frac{5\pi}{2}\right)\right]^2-sin\left(\frac{5\pi}{2}\right)-1\implies 2[1]^2-1-1\implies ?\)

Answer 4

So do I have to solve the bottom equation?

Answer 5

yeap
since we know that \(\bf sin\left(\frac{5\pi}{2}\right) = 1\)
thus we replace that proper numeric value, and solve it, see if it really is equals to 0

Answer 6

yeah it equals zero

Answer 7

:)

Answer 8

So does that mean that the value 5pi/2 is a solution for the equation 2 sin^2 x- sin x - 1 = 0 is TRUE? @jdoe0001

Answer 9

yes

Answer 10

Thank you for your time and help :)

Answer 11

yw