I'm having trouble understanding a sine concept.
For instance, I know that the sine of 15 is .25881. Likewise, the sine of 165 is also .25881. How can I find other values of sine that also equal .25881?
Thank you very much.
This requires an understanding and knowledge about the sine curve and the CAST rule.
The curve repeats every 360º
so if sin 15º=.258819
then sin 375 = .258819
and sin 735 = .258819
and sin (-345) = .258819
in other words you can add or subtract multiples of 360 to 15 and the sine of that angle will be .28819
do the same thing with 165º
I meant to include the webpage on the CAST rule
http://www.physics.uoguelph.ca/tutorials/trig/trigonom2.html
To find other values of sine that equal 0.25881, you can use the inverse sine function, also known as arcsine, or sin^(-1). The inverse sine function takes a value and returns the angle whose sine is that value.
In this case, since you are given the value 0.25881, you can use the inverse sine function to find the angles. However, it's important to note that the inverse sine function typically returns a single angle between -90 degrees and 90 degrees (or -π/2 and π/2 in radians). To obtain other values, you need to consider multiple revolutions around the unit circle.
Here's how you can find additional angles that have a sine equal to 0.25881:
1. Calculate the inverse sine of 0.25881 using a calculator or mathematical software: sin^(-1)(0.25881) ≈ 15 degrees (or 0.26180 radians).
2. Since sine is a periodic function with a period of 360 degrees (or 2π radians), any angle that differs by multiples of 360 degrees (or 2π radians) will have the same sine value.
3. To find other angles, you can add or subtract multiples of 360 degrees (or 2π radians) from the initial angle of 15 degrees (or 0.26180 radians). For example:
- Adding 360 degrees, you get 15 + 360 = 375 degrees (or 0.26180 + 2π ≈ 6.54490 radians).
- Subtracting 360 degrees, you get 15 - 360 = -345 degrees (or 0.26180 - 2π ≈ -6.02033 radians).
- Adding another 360 degrees, you get 375 + 360 = 735 degrees (or 6.54490 + 2π ≈ 12.82780 radians).
- Subtracting another 360 degrees, you get -345 - 360 = -705 degrees (or -6.02033 - 2π ≈ -12.30963 radians).
And so on...
By adding or subtracting multiples of 360 degrees (or 2π radians), you can obtain an infinite number of angles that have the same sine value of 0.25881.