Sin^-1(-√2/2)
To find the value of sin^-1(-√2/2), we first need to understand the concept of the inverse sine function (sin^-1 or arcsin)
To find the value of sin^-1(-√2/2), we first need to understand the concept of the inverse sine function (sin^-1 or arcsin).
The inverse sine function is defined as the angle whose sine is equal to a given value. In other words, sin^-1(x) will give us an angle (in radians or degrees) whose sine is x.
In this case, we are given sin^-1(-√2/2), which means we need to find the angle whose sine is -√2/2.
To do that, we can use the unit circle, which is a circle with a radius of 1 unit. The unit circle is often used in trigonometry to understand the values of sine, cosine, and other trigonometric functions for different angles.
Let’s imagine the unit circle. The point on the unit circle that corresponds to an angle whose sine is -√2/2 is (-√2/2, -1/2). This point is located in the third quadrant, as the sine value is negative and the cosine value is also negative.
Now, we can determine the angle corresponding to this point on the unit circle. To do so, we can use the inverse sine function.
sin^-1(-√2/2) = -π/4 (in radians) or -45° (in degrees).
Therefore, sin^-1(-√2/2) is equal to -π/4 (in radians) or -45° (in degrees).
More Answers:
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Finding the Inverse Sine of -1/2: Calculator and Unit Circle Methods