Question

MAJOR HELP!!!Trigonometric equations: Find all solutions of the equation in the interval 0° ≤ x ≤ 360°.
a) sin 3 Theta = -squrt2 / 2
b) 2sin^2 Theta - cos 2Theta = 0
c) sin2Theta = squrt3 cos 2Theta...HINT: Divide by cos 2Theta

Answer 1

a) sin(x) is -sqrt(2)/2 at 240 and 300, so, you need to divide both of those by 3 to counter-act the multiplication; you'll yield same answer: sin (3(240/3)) = sin(45)
80, 100
b) Not too sure of.
c) sin(2x)/cos(2x)=sqrt(3)
Sin(2x)/cos(2x) is the same as tan(2x). tan(x)=sqrt (3) at pi/3 and 2pi/3= 60 and 120. Same principle as a; since we're multiplying; divide both by 2. 60/2=30 120/2=60
30, 60.

Answer 2

Sorry about reposting twice; I read it wrong and had to correct a typo.

Answer 3

so for a) i started to try and work it out and I see that \[\frac{ -\sqrt{2} }{ 2 } \] is 45 degrees. but its negative so the sine negative would be the 45 deg. in the quadrant 3 and 4. so it gave me 225 degree and 315 degree right?

haha its okay, im trying to understand this whole thing

Answer 4

@JonnyVonny do i understand or did it right?? im going by what I thought haha sorry. Imma look at yours now

Answer 5

here ill draw it out maybe this would help. @JonnyVonny