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
120 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 value of sin(45°) + cos(30°) - tan(60°) when rounded to the nearest hundredth?
+
What is the time taken to travel a distance of 150 km at a speed of 50 km/h?
+
Math question: What is the integral of (3x^2 + 2x + 1) with respect to x?
+
New questions in Mathematics
Jose bought 3/4 of oil and his sister bought 6/8, which of the two bought more oil?
The Lenovo company manufactures laptop computers, it is known that for every 60 laptops produced, 54 go on the market with the highest quality standards. If a sample of 15 laptops is taken, calculate the probability that: Exactly 2 are not of high quality
The actual length of an object is 1.3 m . If the blueprint uses a scale of 1 : 12 , what is the length of the line on the drawing?
The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations. 84. Find the probability that the average price for 30 gas stations is less than $4.55. a 0.6554 b 0.3446 c 0.0142 d 0.9858 e 0
The average number of babies born at a hospital is 6 per hour. What is the probability that three babies are born during a particular 1 hour period?
Solve : 15/16 divide 12/8 =x/y
6-35 A recent study by an environmental watchdog determined that the amount of contaminants in Minnesota lakes (in parts per million) it has a normal distribution with a mean of 64 ppm and variance of 17.6. Assume that 35 lakes are randomly selected and sampled. Find the probability that the sample average of the amount of contaminants is a) Greater than 72 ppm. b) Between 64 and 72 ppm. c) Exactly 64 ppm. d) Greater than 94 ppm.
Given (3x+2)E [2;14] how much money (in soles) does Sophia have if numerically it is the greatest value of x?
A stunt man jumps horizontally from a building to the roof of a garage that is 2 meters lower. How fast does he need to be to land on the roof of the said garage that is 3 meters away from the building?
3.24 ÷ 82
I. Order to add 40.25+1.31+.45 what is the first action to do ?
X³-27
Express the trigonometric form of the complex z = -1 + i.
ind the z-score for which 72% of the distribution's area lies between -z and z. -1.7417, 1.7417 -1.1538, 1.1538 -1.0803, 1.0803 -2.826, 2.826
(a) List the set of possible rational zeros of the polynomial function F(x) = 2x3 - 11x2 + 13x - 4. (b) Find all rational zeros of F(x). Only do part B
A person runs 175 yards per minute write a variable that represents the relationship between time and distance
a) Statistics scores are normally distributed with the mean of 75 and standard deviation of 7. What is the probability that a student scores between 80 and 88
How many cards do you expect to pull from a poker deck until you get an ACE?
Find the rule that connects the first number to the second number of each pair. Apply the rule to find the missing number in the third pair. (18 is to 22) (54 is to 26) (9 is to ?)
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?