Sine example sentences

"Sine" Example Sentences

1. The sine of an angle is the ratio of the opposite side to the hypotenuse.
2. You calculate the sine of an angle using the sin() function in a calculator or programming language.
3. As the angle increases from 0 to 90 degrees, the sine value starts at 0, increases to 1, and then decreases back to 0.
4. The cosine and tangent of an angle can also be calculated using similar trigonometric functions.
5. You must know the measure of an angle in degrees to calculate its sine, cosine, or tangent.
6. A right triangle is useful for visualizing and calculating sine, cosine, and tangent ratios.
7. The Pythagorean Theorem relates the sides of a right triangle to the hypotenuse.
8. In circles, the sine of an angle is equal to the ratio of the y-coordinate of a point on the circle to the radius of the circle.
9. Trigonometric functions find application in physics, engineering, and many other fields that deal with angles and circular motion.
10. You can use a calculator or table of values to look up the exact sine of an angle in degrees.
11. The more acute an angle is, the closer its sine value is to 0.
12. The sine of 45 degrees is equal to the square root of 2 divided by 2, or approximately 0.707.
13. As an angle approaches 90 degrees, its sine value approaches 1.
14. The sine of an angle greater than 90 degrees is the same as the sine of its complementary angle.
15. There are infinite angles with any given sine value between 0 and 1.
16. As an angle approaches 0 or 180 degrees, its sine value approaches 0.
17. You can solve for an unknown side of a right triangle if you know the sine of one of the angles.
18. The units of sine are the same as the ratio it represents—pure numbers with no units.
19. For small angles, the sine and tangent functions are approximately equal to the angle in radians.
20. The tangent of an angle is equal to the sine divided by the cosine of that angle.
21. Her solution involved calculating the sine, cosine and tangent of several angled triangles.
22. The engineer used trigonometric functions to determine the best sine of the wing.
23. The periodic sine wave traces a smooth curve with a regular amplitude and frequency.
24. The sine of an angle cannot be greater than 1 or less than -1.
25. You can graph the values of the sine function as x varies from 0 to 2π.
26. The student carefully calculated the sine, cosine, and tangent of each angle in the problem.
27. The waves oscillate in a regular sine pattern at a consistent frequency.
28. The amplitude of the wave determines the maximum positive and negative values of the sine function.
29. The sine function repeats with a period of 2π and a frequency of 1 cycle per 2π units.
30. Sines and cosines appear everywhere in wave phenomena like sound and light.
31. Vector addition depends on sine and cosine functions to determine the new direction.
32. Their motion followed a predictable sine curve as they swung back and forth.
33. The equations contain sines and cosines to represent the periodic nature of pendulums.
34. She calculated the sine of the angle to determine the y-coordinate of the point.
35. The circuits use sine waves rather than square waves for a smoother output signal.
36. We can approximate the sine curve with a series of straight line segments.
37. The sine of any angle is the y-coordinate of the point where the terminal side of the angle intersects the unit circle.
38. He calculated the sine, cosine, and tangent of several angles to solve the physics problem.
39. The horizontal axis in the sine graph represents the angle in radians, while the vertical axis represents the sine value.
40. Geometric shapes that undergo harmonic motion follow predictable sine and cosine patterns.
41. Amplitude modulation uses the amplitude of a sine wave to represent information.
42. As the frequency of a sine wave increases, its wavelength decreases.
43. The wave forms a smooth sine curve with the amplitude decaying over time.
44. The student graphed the sine function and identified key features like amplitude, wavelength, and period.
45. Combining two or more sine waves of different frequencies produces interesting patterns.
46. The distance an object oscillates is proportional to the amplitude of the driving sine wave.
47. The voltage in an AC circuit follows a sine wave pattern that alternates positive and negative.
48. Sine waves are important for modeling periodic phenomena that oscillate back and forth.
49. As an angle increases from 0 to 90 degrees along the unit circle, its sine value increases linearly from 0 to 1.
50. In general, higher frequencies have shorter wavelengths and vice versa for sine waves.
51. Scientists use sine waves to model oscillations that repeat at regular time intervals.
52. The phase of a sine wave determines where it is in its cycle at any given point in time.
53. The student calculated the sines of several angles to determine their corresponding points on the unit circle.
54. Sine waves are important for modeling sound, which consists of pressure oscillations.
55. The wave simulator produced a smooth sine wave on the display screen.
56. Electrical engineers use sine waves to model alternating current that oscillates back and forth.
57. The coordinates of the point can be determined by calculating the sine and cosine of the angle.
58. Waves in water and other media often follow the smooth shape of a sine curve.
59. The amplitude of a sine wave is the maximum distance of the waveform from the mean value.
60. Summing sine waves with different frequencies produces the graphed waveform.

Common Phases

1. The sine of an angle is calculated using the opposite side and hypotenuse of a right triangle.
2. The sine curve is periodic, repeating every 360 degrees.
3. As the angle increases from 0 to 90 degrees, the sine values increase from 0 to 1.
4. The wave oscillates between positive and negative 1.
5. Sine waves are useful in modeling a variety of periodic phenomena such as sound, light and alternating current.
6. The function sine(x) outputs the sine of the angle x.
7. The function arcsine(x) computes the principle inverse sine of x in radians.
8. He plotted the sine curve on the graph to illustrate the periodic nature of the function.
9. You can approximate the sine of an angle using a Taylor series.
10. She found the sine, cosine and tangent of 45 degrees using a calculator.
11. Trigonometric tables list the sine, cosine and tangent values for common angles.
12. The components of an AC circuit change periodically as modeled by sine waves.
13. The loudness of sound waves can be represented by the amplitude of a sine wave.
14. The human ear perceives the pitch of a sound based on the frequency of its sine wave.
15. The phase of a sine wave determines where it is in its cycle relative to a reference point.
16. Ocean tides are often modeled as the sum of multiple sine waves.
17. Music synthesizers use combinations of sine waves at different frequencies and amplitudes.
18. He derived the formula for calculating the sine of an angle using a unit circle.
19. Engineers use transformation of sine functions to solve differential equations.
20. The solution he arrived at involved taking the sine of both sides of the equation.
21. The professor explained how to evaluate limits involving sine functions.
22. Sine waves are special cases of trigonometric functions.
23. They studied how to graph sine functions by translating and reflecting.
24. Amplitude modulation in radio uses a sine wave to encode information.
25. The wave nature of light is modeled using sine and cosine functions.
26. Oscillating electric currents in an LRC circuit follow a sine function.
27. We derived an expression for the function f(x) = sin(x) - cos(x).
28. She calculated the integral of the sine function from 0 to pi.
29. Amplitude, frequency and phase are parameters of any sine wave function.
30. The servo motor's position is controlled by a sine wave input signal.
31. They learned how to write Maclaurin and Taylor series for the sine function.
32. The instructor taught the class how to use sine and cosine to solve triangles.
33. You can add and multiply sine functions using trigonometric identities.
34. As the frequency increases, the period of the sine wave decreases.
35. The engineer used approximations of sine functions in her circuit design.
36. We applied integration by parts to evaluate the integral of sine squared x.
37. The wave equation involves both the sine and cosine functions.
38. The simulation modeled the motion of a pendulum using a sine function.
39. The amplitude spectrum shows the frequency components of a signal or sine wave.
40. A square wave can be approximated by summing several sine waves.
41. The equation of simple harmonic motion involves sine or cosine functions.
42. The input voltage to the op amp circuit was a 20 Hz sine wave.
43. We convolved two sine wave functions together to get their product.
44. The animator used simple sine waves to simulate the motion of jelly.
45. A damped sine wave is a sine wave whose amplitude decreases over time.
46. Summing two sine waves creates a phenomenon known as beats.
47. The phase difference between two sine waves determines their interference pattern.
48. The harmonics of a signal are sine waves with frequencies that are integer multiples of the fundamental frequency.
49. The impedance of an inductor in an AC circuit depends on the frequency of the driving sine wave.
50. Two objects vibrating with the same frequency but different phases will produce a "beat frequency" when summed.
51. A Halbach array consists of arranging permanent magnets to produce a sine wave magnetic field.
52. The coil of an electromagnet produces a magnetic field that varies according to a sine wave.
53. The fundamental mode of a vibrating string corresponds to a sine wave with one node.
54. The noise produced when two out-of-phase sine waves are summed is known as beat noise.
55. A frequency generator can produce sine waves at specific frequencies under microprocessor control.
56. You can convert a square wave signal into sine waves of different frequencies using a Fourier series.
57. The current through an inductor changes linearly with the applied sine voltage.
58. The Wiener-Khinchin theorem relates the power spectral density of a signal to the autocorrelation of its sine waves.
59. The driven damped harmonic oscillator's steady state behavior follows a sine function.
60. I learned about Fourier analysis and how any wave can be constructed from sine waves.