plz help plz plz/ trigonometry?

Question

Solve. Give all positive values of the angle between 0º and 360º that will satisfy each. Give any approximate value to the nearest minute only.

1. sin 2 0 = √3/2
2. sin 2x – cos x =0
3. sin ( 2x - 10º ) = ½
4. cos 4x=sin 2x


thks

Answer 1

I assume you mean solve for x.

1. sin 2 0 = √3/2
This doesn't make sense; there is no x.

2. sin 2x – cos x =0
sin 2x = cos x
2(sin x)(cos x) = cos x
2sin x = 1
sin x = 1/2
x = 30°, 150°

3. sin (2x - 10º) = ½
2x - 10 = 30, 150
2x = 40, 160
x = 20°, 80°

4. cos 4x = sin 2x
1 - 2sin²2x = sin 2x
2sin²2x + sin 2x - 1 = 0
(2sin 2x - 1)(sin 2x + 1) = 0
sin 2x = 1/2, -1
2x = 30°,150°,270°
x = 15°,75°,135°

Answer 2

ANS2: cosec^2 x - sec^2 x =(cot² x+a million)-(tan² x+a million) =a million/tan² x - tan² x ANS3: a) sin² B - cos² B = sin² B - (a million - sin² B) =2sin² B - a million b) (a million – cos² y + sin² y)² +4 sin² y cos² y = (a million - 2cos² y + 2sin² y - 2sin² y cos² y + cos^4 y + sin^4 y) +4 sin² y cos² y = a million - 2cos² y + 2sin² y + 2sin² y cos² y + cos^4 y + sin^4 y = a million - 2cos² y + 2sin² y + (sin² y + cos²y)² = 2 - 2cos² y + 2sin² y = 4sin² y c) tan 0 = 0 sec 0 = a million hence tan² 0 sec² 0- sec² 0+a million d)sin 0/cosec0 + cos 0/sec0 =sin 0/a million/sin 0 + cos 0/a million/cos 0 =sin² 0 + cos² 0 =a million = 0 - a million + a million = 0 = tan 0 e)sin x tan ² x cot ^3 x = sin x cot x = sin x (cos x/sin x) = cos x f)sec² x/(sec ² x-a million) = a million/cos² xtan² x = a million/sin² x = cosec² x

Answer 3

think hard & pay attention