If cos theta =-2/3, which of the following are possible
1 answer:
Well, the cos(∅) is negative in the second and third quadrants. If you are solving for theta, you would use the inverse of the cos or arccos
take the inverse of both sides to get:
x = arccos(-2/3) now evaluate the right
x = 131.8103149 degrees
to find your second solution, subtract your reference angle from 360 degrees.
360 - 131.8103149 = 228.1896851 degrees
Now the period of cos is 2π or 360 degrees. So if you want to consider all possible solutions, you would need to add/subtract 360n to both solutions above..
Not sure if this is what you're looking for, but thought I would leave it here for you just in case... As a side note, you could do this problem in radian measurement as well.
x = arccos(-2/3) now evaluate the right
x = 131.8103149 degrees
to find your second solution, subtract your reference angle from 360 degrees.
360 - 131.8103149 = 228.1896851 degrees
Now the period of cos is 2π or 360 degrees. So if you want to consider all possible solutions, you would need to add/subtract 360n to both solutions above..
Not sure if this is what you're looking for, but thought I would leave it here for you just in case... As a side note, you could do this problem in radian measurement as well.
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Answer:
x = - , x =
Step-by-step explanation:
Given
x² - x - = 0
Multiply through by 4 to clear the fraction
4x² - 4x - 3 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × - 3 = - 12 and sum = - 4
The factors are + 2 and - 6
Use these factors to split the x- term
4x² + 2x - 6x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(2x + 1) - 3(2x + 1) = 0 ← factor out (2x + 1) from each term
(2x + 1)(2x - 3) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = -
2x - 3 = 0 ⇒ 2x = 3 ⇒ x =