Which angle is a solution of:
2 sin 2x - 1 = 0
Select the appropriate response:
A) 180°
B) 120°
C) 225°

50 POINTS

Answer and Step-by-step explanation:

Let's solve this like a regular equation:

2sin(2x) - 1 = 0

2sin(2x) = 1

sin(2x) = 1/2

Replace 2x with y:

sin(y) = 1/2

What angles for y will make this true? Think to the unit circle; the possible angles are 30° and 150°.

Then, x = 30/2 = 15°or 150/2 = 75°.

(Note that none of the answer choices matches, so the problem/choices may be copied incorrectly)

C) 225°

Step-by-step explanation:

2sin²x = 1

sin²x = ½

sinx = +/- 1/sqrt(2)

Basic angle: 45°

In one complete cycle,

45, 180-45, 180+45, 360-45

45°, 135°, 225°, 315°

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3