calculus help needed
example: sin-1(-1/2)
how do you figure this out?
The sin^-1 means the arcSin, or the angle whose sine is ...
so sin^-1(1/2) is the angle whose sine is -.5, which is -30 degrees.
In your calculator, put in -.5, then press INV sin.
so as my answer do i put pi/6?
That is the answer in radians. It should be negative. There is an angle in the third quadrant that yields a sine of -1/2 also.
To figure out the value of sin^-1(-1/2), you can follow these steps:
1. Understand the notation: sin^-1(x) represents the inverse sine function or the arc sine function. It gives the angle whose sine is x. In other words, sin^-1(x) = θ means sin(θ) = x.
2. Identify the value of x: In this case, x is -1/2.
3. Calculate the angle: To find the angle whose sine is -1/2, you can use a scientific calculator. Input -1/2 as -0.5 in the calculator and then press the INV or SIN^-1 button to calculate the inverse sine or arc sine function.
4. Determine the answer: Depending on the mode your calculator is set to (degrees or radians), you will get the value of the angle in either degrees or radians. The answer in radians is -π/6, and the answer in degrees is -30°.
5. Verify the answer: Since the sine function is periodic, it repeats its values after every 2π radians or 360 degrees. Therefore, there is an angle in the third quadrant (-π/2 to -π) that also yields a sine of -1/2. In this case, the angle -π/6 is appropriate as it falls within the desired range and matches the given value. Hence, your answer can be either -π/6 or -30°.