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
85 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)
What is the limit of (3x^2 + 5) / (2x + 1) as x approaches 3?
+
What is the standard deviation of a dataset where the values are 5, 9, 12, 15, and 20?
+
Find the measure of a complementary angle if its supplement is 75 degrees.
+
New questions in Mathematics
Solution to the equation y'' - y' - 6y = 0
Solve: −3(−2x+23)+12=6(−4x+9)+9.
If O(3,-2) is reflected across x = 2. What are the coordinates of O
The length and breadth of my rectangular vegetable garden is 12,5m and 7,25m respectively. What is the perimeter of the garden?
Elliot opened a savings account and deposited $5000.00 as principal. The account earns 4% interest, compounded annually. How much interest will he earn after 5 years? Round your answer to the nearest cent.
In a store there are packets of chocolate, strawberry, tutti-frutti, lemon, grape and banana sweets. If a person needs to choose 4 flavors of candy from those available, how many ways can they make that choice?
Two events E and F are​ ________ if the occurrence of event E in a probability experiment does not affect the probability of event F.
Suppose 50% of the doctors and hospital are surgeons if a sample of 576 doctors is selected what is the probability that the sample proportion of surgeons will be greater than 55% round your answer to four decimal places
Divide 22 by 5 solve it by array and an area model
calculate the normal vector of line y = -0.75x + 3
If f(x,y)=6xy^2+3y^3 find (∫3,-2) f(x,y)dx.
Let A, B, C and D be sets such that | A| = |C| and |B| = |D|. Prove that |A × B| = |C × D|
The simple average of 15 , 30 , 40 , and 45 is
-1%2F2x-4%3D18
In a physics degree course, there is an average dropout of 17 students in the first semester. What is the probability that the number of dropouts in the first semester in a randomly selected year has between 13 and 16 students?
17. A loan for $104259 is taken out for 10 years with an annual interest rate of 9.4%, compounded quarterly. What quarterly payment is required to pay the loan off in 10 years? Enter to the nearest cent (two decimals). Do not use $ signs or commas in the answer.
A multiple choice exam is made up of 10 questions; Each question has 5 options and only one of them is correct. If a person answers at random, what is the probability of answering only 3 good questions?
Translate to an equation and solve. Let x be the unknown number: What number is 52% of 81.
A buyer purchased a North Carolina home for $475,250. The seller allowed the buyer to assume his first small mortgage with a loan balance of $110,000. How much is the excise tax paid in the transaction? $951 $729.50 $950.50 $221 none of the above
A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 55.0 min at 100.0 km/h, 14.0 min at 65.0 km/h, and 45.0 min at 60.0 km/h and spends 20.0 min eating lunch and buying gas. (a) Determine the average speed for the trip.