The cosine of an angle is the x-coordinate of the point where its terminal ray intersects the unit circle. So, we can draw a line at x=-1/2 and see where it intersects the unit circle. That will tell us possible values of θ/2.
We find that vertical line intersects the unit circle at points where the rays make an angle of ±120° with the positive x-axis. If you consider only positive angles, these angles are 120° = 2π/3 radians, or 240° = 4π/3 radians. Since these are values of θ/2, the corresponding values of θ are double these values.
a) The cosine values repeat every 2π, so the general form of the smallest angle will be
... θ = 2(2π/3 + 2kπ) = 4π/3 + 4kπ
b) Similarly, the values repeat for the larger angle every 2π, so the general form of that is
... θ = 2(4π/3 + 2kπ) = 8π/3 + 4kπ
c) Using these expressions with k=0, 1, 2, we get
... θ = {4π/3, 8π/3, 16π/3, 20π/3, 28π/3, 32π/3}
Answer:
{y,x} = {-6,-2}
Step-by-step explanation:
/ Solve equation [2] for the variable y
[2] y = 2x - 2
// Plug this in for variable y in equation [1]
[1] (2x-2) - x = -4
[1] x = -2
// Solve equation [1] for the variable x
[1] x = - 2
// By now we know this much :
y = 2x-2
x = -2
// Use the x value to solve for y
y = 2(-2)-2 = -6
Answer:
1. a + b + c = 180
2. b + d = 180
3. d = a + c
Step-by-step explanation:
1. a + b + c = 180:
Angles in a triangle add up to 180
2. b + d = 180:
Angles in a straight line equal 180 because they are supplementary angles
3. d = a + c:
ΔACD is an exterior angle, and ΔACB is interior adjacent, hence ∠a and ∠c add up to ∠d
$4 is the original price of the jar consisting of peanut butter so therefor it = 100%. It's for sale at $3.60, so we divide $4 by 100% so we get the percentage for each cent and then we times it by 3.60 to get the percentage for $3.60 which is 90%. Now we subtract 90% from 100% to get the discounted percentage for 40cents :)
This is a square root meaning whatever number multiplied by itself equals it’s square root. The answer would be 4 on the outside and 3 on the inside
