Question

Solve the equation sin 2x - sin x = 0

270

likes
1352 views

Answer to a math question Solve the equation sin 2x - sin x = 0

Expert avatar
Fred
4.4
118 Answers
To solve the equation sin 2x - sin x = 0, we will use the trigonometric identity sin 2x = 2sin x cos x.

Substitute sin 2x = 2sin x cos x into the equation:
2sin x cos x - sin x = 0

Factor out sin x:
sin x(2cos x - 1) = 0

Now, we have two possibilities:
1) sin x = 0
2) 2cos x - 1 = 0

For sin x = 0:
x = kπ, where k is an integer.

For 2cos x - 1 = 0:
2cos x - 1 = 0
2cos x = 1
cos x = 1/2

Using the unit circle or the knowledge of cosine function values, we find x = π/3 + 2πk or x = 5π/3 + 2πk, where k is an integer.

Therefore, the solutions are:
x = kπ, x = π/3 + 2πk, x = 5π/3 + 2πk, where k is an integer.

\boxed{x = k\pi, \quad x = \frac{\pi}{3} + 2k\pi, \quad x = \frac{5\pi}{3} + 2k\pi, \quad \text{where } k \text{ is an integer}}

Frequently asked questions (FAQs)
Math question: What is the slope-intercept equation of a line that passes through the points (-2, 5) and (4, -3)?
+
What is the mode of the following data set: 5, 7, 3, 7, 8, 5, 7?
+
What is the slope of the linear function f(x)=x?
+
New questions in Mathematics
Let f(x)=||x|−6|+|15−|x|| . Then f(6)+f(15) is equal to:
Solution of the equation y'' - y' -6y = 0
Simplify the expression sin³(x)+cos³(x), using trigonometric functions
Karina has a plot of 5000 square meters in which she has decided that 60% of it will be used to plant vegetables. Of this part, 12% will be dedicated to planting lettuce. How much surface area of the plot will be used to grow lettuce?
what is 3% of 105?
5) A family with a father, mother and 3 children must sit on five chairs in a row and the only restriction is that the mother must be at one end. In how many different ways can they be seated?
The length and breadth of my rectangular vegetable garden is 12,5m and 7,25m respectively. What is the perimeter of the garden?
The mean temperature for july in H-town 73 degrees fahrenheit. Assuming that the distribution of temperature is normal what would the standart deviation have to be if 5% of the days in july have a temperature of at least 87 degrees?
Subscribers to the FAME magazine revealed the following preferences for three categories: Fashion 30, Athletics 24 and Business 15. Following these frequencies of observation, compute the chi-square test statistic. At the 0.05 level of significance, would you conclude they are similar?
4x + 8y = 5 2x + 4y = 10
Log5 625
sin 30
reduce the expression (7.5x 12)÷0.3
P(Z<z)=0.1003
A teacher has 25 red and yellow counters altogether. She has 4 times as many red counters than yellow counters. How many yellow counters does the teacher have?
List five numbers that belong to the 5 (mod 6) numbers. Alternate phrasing, list five numbers that satisfy equation x = 5 (mod 6)
effectiveness of fiscal and monetary policy under closed and open economies
Solve the following system of equations using substitution. y=-4x- 11. 3x+7y=-2
Find the symmetric point to a point P = (2,-7,10) with respect to a plane containing a point Po = (3, 2, 2) and perpendicular to a vector u = [1, -3, 2].
An invoice for €2,880 plus default interest of €48.40 was paid on October 28th. Interest rate 5.5%. When was the bill due?