Write the general solution to y = arcsin (0.6428).
40°±360°k
140°±360°k
220°±360°k
320°±360°k
40 +/- 360k
Most arcsin solutions follow with 2pik or 360k.
arcsin functions can only fall within -90 and 90 degrees, so 40 can be your only answer, even if you choose to scale the answer.
Well, aren't you lucky! I have the perfect solution for you, wrapped in a little bit of humor. So, the general solution to y = arcsin(0.6428) is like a big circus filled with rotating clowns. Ready for the show? Here it goes:
The general solution is expressed as 40° ± 360°k, 140° ± 360°k, 220° ± 360°k, and 320° ± 360°k.
In this wacky circus, the main event is the angle y, which takes on the value of 0.6428 in its arcsine form. And just like clowns spinning on unicycles, the solutions rotate around the original angles every 360°. So, imagine you're in the front row of this eccentric circus, witnessing the madness of the angles at 40°, 140°, 220°, and 320°. Now, before you get dizzy, remember that 'k' represents any integer that can be thrown into our circus equation.
So, now you can step into this wacky circus called math and enjoy the vibrant, rotational world of solutions! Ta-da! 🎪
To find the general solution for the equation y = arcsin (0.6428), we first need to determine the angle whose sine is 0.6428.
Using a calculator, we can calculate the arcsin (0.6428) ≈ 40.03°.
The general solution to the equation y = arcsin (0.6428) is given by the formula:
y = 40° ± 360°k,
where k is an integer that represents the number of complete revolutions around the unit circle.
Therefore, the general solution is:
40° ± 360°k,
where k is an integer.
To find the general solution for y = arcsin(0.6428), we need to consider the range of the arcsin function. The arcsin function has a range of [-π/2, π/2] or approximately [-1.57, 1.57] in radians, or [-90°, 90°] in degrees.
First, calculate the arcsin(0.6428) using a calculator, which gives you approximately 40°.
Since the sine function is periodic with a period of 360°, you can determine that adding or subtracting multiples of 360° will give you additional solutions.
So, to obtain the general solution, you need to add or subtract multiples of 360° (or 2π radians) from the initial solution. Therefore, the general solution is given by:
y = 40° ± 360°k, where k is an integer.
This means that for every integer value of k, you can obtain a valid solution by adding or subtracting 360° (or any multiple of 360°) to the initial solution of 40°.
So the general solution for y = arcsin(0.6428) is:
y = 40° ± 360°k, where k is an integer.
Furthermore, the specific solutions you provided (140°±360°k, 220°±360°k, 320°±360°k) are not valid solutions because they fall outside the range of [-90°, 90°], which is the valid range for the arcsin function.