Calculus
Trigonometry

# How do you solve x equals 2 sin x?

###### Wiki User

The problem x = 2 sin x cannot be solved by using algebraic methods.

One solution is to draw the graphs of y = x and y = 2 sin x.

The two lines will intersect. The values of x where the intersection takes place are the solutions to this problem.

You can tell from the graph that one solution is x=0 and verify this contention by noting that 2 sin(0) = 0.

You can find the other solution through numerical methods and there are many that will give you the correct solution. Perhaps the simplest is to start with a value of X like pi/2 and then take the average of 2*sin(X) and X. Using that as your new value, again take the average of 2*sin(X) and X. As you continue to do this, the value will get closer and closer to the desired value. After 20 steps or so, the precision of your calculator will probably be reached and you will have a pretty good answer of about 1.89549426703398. (A spreadsheet can be used to make these calculations pretty easily.)

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## Related Questions

3 sin(x) = 2sin(x) = 2/3x = 41.81 degreesx = 138.19 degrees

Sin(2x) = -cos(x)But sin(2x) = 2 sin(x) cos(x)Substitute it:2 sin(x) cos(x) = -cos(x)Divide each side by cos(x):2 sin(x) = -1sin(x) = -1/2x = 210&Acirc;&deg;x = 330&Acirc;&deg;

2*sin^2(x) - 5*sin(x) + 2 = 0 is a quadratic equation in sin(x).therefore,{2*sin(x) - 1}*{sin(x) - 2)} = 0=> sin(x) = 1/2 or sin(x) = 2The second solution is rejected since sin(x) cannot exceed 1.The principal solution is x = arcsin(1/2) = pi/6 radians. Additional or alternative solutions will depend on the domain for x - which has not been given.

Do sin(x), square it, and then multiply it by two.

2 sin2 x + sin x = 1. Letting s = sin x, we have: 2s2 + s - 1 = (2s - 1)(s + 1) = 0; whence, sin x = &frac12; or -1, and x = 30&deg; or 150&deg; or 270&deg;. Or, if you prefer, x = &pi;/6 or 5&pi;/6 or 3&pi;/2.

they do have calculators for these questions you knowsin 2x = (sin x)/22 sin x cos x - (1/2)sin x = 02 sin x(cos x - 1/4) = 02 sin x = 0 or cos x - 1/4 = 0sin x = 0 or cos x = 1/4in the interval [0, 360)sin x = 0, when x = 0, 180cos x = 1/4, when x = 75.52, 284.48Check:

First write everything in terms of sines and cosines.2 sin x / cos x - (1 / cos x)2 = 0Multiply by the common denominator, cos2x:2 sin x cos x - 1 = 0Solve:2 sin x cos x = 1sin 2x = 12x = pi/2, or 2x = 5pi/2, or 2x = 9pi/2...For the first one, 2x = pi/2 --> x = pi/4.

Assuming the question refers to [sin(x)]/2 rather than sin(x/2) the answer is 1.

(2 sin^2 x - 1)/(sin x - cos x) = sin x + cos x (sin^2 x + sin^2 x - 1)/(sin x - cos x) =? sin x + cos x [sin^2 x - (1 - sin^2 x)]/(sin x - cos x) =? sin x + cos x (sin^2 x - cos^2 x)/(sin x - cos x) =? sin x + cos x [(sin x - cos x)(sin x + cos x)]/(sin x - cos x) =? sin x + cos x sin x + cos x = sin x + cos x

There is nothing to solve in this equation because there is no =. If you accidentally omitted what the expression equals then resubmit it and I'll be happy to look at it

To solve 2 cos2x + sin x - 1 make use of the identity cos2x + sin2x = 1, then: cos2x = 1 - sin2x and 2 cos2x + sin x - 1 = 2 (1 - sin2x) + sin x - 1 = 2 - 2 sin2x + sin x - 1 = 1 + sin x - 2 sin2 x if you let y = sin x, then you can see you have a quadratic: 1 + sin x - 2 sin2 x = 1 + y - 2y2 which can be solved for 1 + y - 2y2 = 0: 1 + y - 2y2 = 0 &rArr; 2y2 - y - 1 = 0 &rArr; (2y + 1)(y - 1) = 0 &rArr; y = -1/2 or 1 but y = sin x, so: sin x = -1/2 or sin x = 1 and so solve these for x.

sec x - cos x = (sin x)(tan x) 1/cos x - cos x = Cofunction Identity, sec x = 1/cos x. (1-cos^2 x)/cos x = Subtract the fractions. (sin^2 x)/cos x = Pythagorean Identity, 1-cos^2 x = sin^2 x. sin x (sin x)/(cos x) = Factor out sin x. (sin x)(tan x) = (sin x)(tan x) Cofunction Identity, (sin x)/(cos x) = tan x.

Yes. sin(A+B) = sin A cos B + cos A sin B If A = B = x, this becomes: sin(x+x) = sin x cos x + cos x sin x &rarr; sin 2x = 2 sin x cos x

2 sin2(x) + sin(x) - 1 = 0(2 sin + 1) (sin - 1) = 0Either 2 sin(x) + 1 = 02sin(x) = -1sin(x) = -0.5x = 210&Acirc;&deg;, 330&Acirc;&deg;or sin(x) - 1 = 0sin(x) = 1x = 90&Acirc;&deg;

Cos x = 1 / Sec x so 1 / Cos x = Sec x Then Tan x = Sin x / Cos x = Sin x * (1 / Cos x) = Sin x * Sec x

A*sin(x) + cos(x) = 1B*sin(x) - cos(x) = 1Add the two equations: A*sin(x) + B*sin(x) = 2(A+B)*sin(x) = 2sin(x) = 2/(A+B)x = arcsin{2/(A+B)}That is the main solution. There may be others: depending on the range for x.

2 sin(x) - 3 = 0 2 sin(x) = 3 sin(x) = 1.5 No solution. The maximum value of the sine function is 1.0 .

The amplitude of the wave [ y = -2 sin(x) ] is 2.

You can't. tan x = sin x/cos x So sin x tan x = sin x (sin x/cos x) = sin^2 x/cos x.

cos x - 2 sin x cos x = 0 -&gt; cos x (1 - 2 sin x) = 0 =&gt; cos x = 0 or 1 - 2 sin x = 0 cos x = 0: x = &pi;/2 + k&pi; 1 - 2 sin x = 0: sin x = 1/2 -&gt; x = &pi;/6 + 2k&pi; or 5/6&pi; + 2k&pi; Thus x = &pi;/2 + k&pi;; x = &pi;/6 + 2k&pi;; x = 5/6&pi; + 2k&pi; solve the original equation.

Assuming the angles are expressed in radians:sin(5x) + sin(x) = 0&there4; sin(5x) = -sin(x)&there4; 5x = x + &pi;&there4; x = &pi;/4On the other hand, if your angles are in degrees, then the answer would be:sin(5x) + sin(x) = 0&there4; sin(5x) = -sin(x)&there4; 5x = x + 180&there4; x = 180&deg;/4&there4; x = 45&deg;

sin x/(1+cos x) + cos x / sin x Multiply by sin x (1+cos x) =[(sin^2 x + cos x(1+cos x) ] / sin x (1+cos x) = [(sin^2 x + cos x + cos^2 x) ] / sin x (1+cos x) sin^2 x + cos^2 x = 1 = (1+cos x) / sin x (1+cos x) = 1/sin x

x = 45 degrees sin(x) = cos(x) = 1/2 sqrt(2)