solve for (<_ = less than or equal to / pie = pie sign / -pie = negative pie)

Question

3 sin²x = cos²x ; 0 <_ x < 2pie
cos²x - sin²x = sinx ; -pie < x <_ pie

Answer 1

1st one:

3 sin²x = cos²x ; 0 ≤ x < 2π
sin²x /cos²x = 1/3
tan^2 x = 1/3
tanx = ± 1/√3
set your calculator to radians ....
x = .5236
x = π - .5236 = 2.61799
x = π + .5236 = 2.61799
x = 2π- .5236 = 5.7596

2nd:
cos^2 x - sin^2 x = sinx
1 - sin^2 x - sin^2 x - sinx = 0
2sin^2 x + sinx - 1 = 0
(2sinx -1)(sinx + 1) = 0
sinx = 1/2 or sinx = -1

if sinx = 1/2
x = π/6, or x = 5π/6
if sinx = -1
then x = =π/2 or 3π/2 ,but -π < x ≤ π
so x = -π/2

x = -π/2 , π/6 , 5π/5

Answer 2

Thank you Reiny! The first question (1st one) your calculations for the 2nd x is wrong. x = x = π + .5236 = 3.665192654 and not 2.61799

Answer 3

yup, clearly a typo, since the first part of it is correct