Solve the equation 2 cos ( x ) + 1 = 0 2 cos x + 1 = 0 , 0 ≤ x ≤ 2 π 0 ≤ x ≤ 2 π . Show all of your work
1 answer:
Answer:
2π/3, 4π/3
Step-by-step explanation:
I interpret your question as asking us to solve the equation
2cos(x) + 1 = 0
2cos(x) = -1
cos(x) = -½x
x = arccos(-½), 0 ≤ x ≤2π
Since the cosine is negative, x must be in the second or third quadrant.
Referring to the unit circle, we find that
x = 2π/3 (120°) or x = 4π/3 (240°)
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Answer:
y = - x -
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m =
with (x₁, y₁ ) = (- 4, 2 ) and (x₂, y₂ ) = (3, - 4) ← 2 points on the line
m = = -
, thus
y = - x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 4, 2 ), then
2 = + c ⇒ c = 2 -
= -
y = - x -
← equation of line