Question

Solve the equation sin 2x - sin x = 0

270

likes1352 views

Fred

4.4

63 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}}

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.

Frequently asked questions (FAQs)

Math question: If a shirt costs $30 and is on sale for 20% off, how much will the shirt cost after the discount? (

+

What is the equation of a parabola with its vertex at (2,5) and opening downwards?

+

What is the correlation coefficient between the hours studied and exam scores of 50 students?

+

New questions in Mathematics