cos(2 x) + 2 = sin(x)
Solve for x over the real numbers:
sin(x) - cos(2 x) = 2
Transform sin(x) - cos(2 x) into a polynomial with respect to sin(x) using cos(2 x) = 1 - 2 sin^2(x):
-1 + sin(x) + 2 sin^2(x) = 2
Divide both sides by 2:
-1/2 + sin(x)/2 + sin^2(x) = 1
Add 1/2 to both sides:
sin(x)/2 + sin^2(x) = 3/2
Add 1/16 to both sides:
1/16 + sin(x)/2 + sin^2(x) = 25/16
Write the left hand side as a square:
(sin(x) + 1/4)^2 = 25/16
Take the square root of both sides:
sin(x) + 1/4 = 5/4 or sin(x) + 1/4 = -5/4
Subtract 1/4 from both sides:
sin(x) = 1 or sin(x) + 1/4 = -5/4
Take the inverse sine of both sides:
x = 2 π n + π/2 for n element Z
or sin(x) + 1/4 = -5/4
Subtract 1/4 from both sides:
x = 2 π n + π/2 for n element Z
or sin(x) = -3/2
sin(x) = -3/2 has no solution since for all x element R, -1<=sin(x)<=1 and -3/2<-1:
Answer: |
| x = 2 π n + π/2 for n element Z
<u>x = 1/2 (4 π n + π)</u> n element Z
Answer:
This point is not on the line, NOT TRUE
Step-by-step explanation:
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
b represents the y-intercept
where the format of a point is (x, y)
<u>Given:</u> y = 7x (6/7, -1/4)
we can plug in the point (6/7, -1/4)
-1/4 = 7(6/7)
-1/4 = 6
<em>-1/4 does not equal 6 so this point is not on the line</em>
Learn more about slope and y-intercept here: brainly.com/question/12763756
2x -3y = 13
4x -y = -9
Multiply the second equation by -3 to make the coefficient of Y opposite the first equation.
4x -y = -9 x -3 = -12x + 3y = 27
Now add this to the first equation:
2x -12x = -10x
-3y +3y = 0
13 +27 = 40
Now you have :
-10x = 40
Divide each side by -10:
x = 40 / -10
x = -4
Now you have a value for x, replace that into the first equation and solve for y:
2(-4) - 3y = 13
-8 - 3y = 13
Add 8 to both sides:
-3y = 21
Divide both sides by -3:
y = 21/-3
y = -7
Now you have X = -4 and y = -7
(-4,-7)
Answer:
The answer to your question is
A = 29.6°
B = 115.4°
C = 35°
Step-by-step explanation:
Process
1.- Use the Cosines law to answer this question
c² = a² + b² - 2abcosФ
Solve for cos Ф
cos Ф = (c² - a² - b² )/ -2ab
Substitution
cosФ = (7² - 6² - 11²) / (-2)(6)(11)
cosФ = (49 - 36 - 121) / -132
cos Ф = -108 / -132
cos Ф = 0.818
Ф = 35° = C
Find B
cos Ф = (b² - a² - c²) / (-2ac)
cos Ф = (11² - 6² - 7²) / (-2)(6)(7)
cos Ф = ( 121 - 36 - 49) / -84
cos Ф = 36 / -84
cos Ф = -0.429
Ф = 115.4° = B
2.- Find a
The sum of the internal angles in a triangle equals 180°
A + B + C = 180
A + 115.4 + 35 = 180
A = 180 - 115.4 - 35
A = 29.6°