Find the values of x for which the equation sin x = -1 is true
2 pi n
pi/2 + 2 pi n
pi + 2 pi n
3 pi/2 +2 pi n
Can someone please help. I don't understand how to do this.
Sin x = -1 when x is 270 degrees, which is 3 pi/2 radians. If you add (2 n pi) to that, where n is an integer, you get the same value for the sin.
Therefore the correct answer is the last one.
To find the values of x for which the equation sin x = -1 is true, you need to consider the unit circle and the values of sin x.
The unit circle is a circle with a radius of 1 centered at the origin (0,0) on a coordinate plane. sin x represents the y-coordinate of a point on the unit circle, given an angle x.
Since sin x = -1, we are looking for the angles that correspond to a y-coordinate of -1 on the unit circle.
The values of x for sin x = -1 can be found at the angles where the unit circle intersects with the line y = -1.
Based on the unit circle, we can see that the angle x where sin x = -1 is pi radians or 180 degrees.
However, we need to consider that the sine function has a periodicity of 2 pi, meaning it repeats every 2 pi radians or 360 degrees.
Therefore, we can determine that the values of x for which the equation sin x = -1 is true can be expressed as:
x = pi + 2 pi n, where n is an integer.
This indicates that x can be pi, pi + 2 pi, pi + 4 pi, and so on.
So, the correct answer is:
pi + 2 pi n, where n is an integer.
To find the values of x for which the equation sin x = -1 is true, we need to determine the values of x that satisfy this equation.
The equation sin x = -1 represents the equation of the sine function, where the output (y-values) is -1. In the unit circle, the sine function outputs -1 at two specific angles: -π/2 and -3π/2. However, we need to find all the angles that satisfy the equation sin x = -1.
In the unit circle, the sine function repeats its values every 2π radians, completing one full cycle. Therefore, any angle x that satisfies the equation sin x = -1 can be expressed in the following form:
x = -π/2 + 2πn, where n is an integer.
By substituting different values of n, you can find all the angles that satisfy the equation sin x = -1.
To summarize, the values of x that satisfy the equation sin x = -1 can be written in the form:
x = -π/2 + 2πn, where n is an integer.