Find all solutions to the equation. (1 point) sin x = square root of three divided by two.

x=pi/3 + 2pi*k

x=2pi/3+2pi*k

Step-by-step explanation:

sin(x)=sqrt(3)/2

This happens twice in the first rotation on our unit circle.

It happens in the first quadrant and in the second quadrant. Third and fourth quadrants are negative for sine.

So we are looking for when the y-coordinate on the unit circle is sqrt(3)/2.

This is at pi/3 and 2pi/3.

So we can get all the solutions by adding +2pi*k to both of those.  This gives us a full rotation about the circle any number of k times. k is an integer.

So the solutions are

x=pi/3 + 2pi*k

x=2pi/3+2pi*k

multiply length by height. multiply the length by the height, and then double the product. work out 10 x 10 results = 100 square inches, then work out 100 x 2 = 200. the answer is 200 square inches.

step-by-step explanation:

answer: integers are just whole numbers: positive, negative, and zero.

i = {-∞, -2, -1, 0, 1, 2, 3, ∞}

let x = 1st integer

let y = 2nd integer

x = 3y + 17   {equation 1}

xy = -24         {equation 2}

substitute 3y+17 in place of x n equation 2

and solve for y.

(3y+17)y = -24

3y2 + 17y = -24

3y2 + 17y + 24 = 0

from quadratic equation:

y = [-17±√(172-4(3)(24))]/(2(3))

y = (-17 ±√1)/6

y = (-17+1)/6   or     y = (-17-1)/6

y = -16/6           or     y = -18/6

y = -2 2/3         or   y = -3

since we are dealing with

y = -3

x = 3y+17 = -9+17 = 8

the integers are -3, 8

step-by-step explanation: