For questions 2 and 3, use a calculator to find the values of the inverse function in radians.
sin^-1(0.65)
0.71 + 2pi n and –0.71 + 2 pi n
0.71 + 2 pi n and –3.85 + 2 pi n
0.86 + 2pi n and –0.86 + 2pi n
–0.61 + 2pi n and 2.54 + 2 pi n
tan^-1(-0.09)
–0.09 + 2pi n
No such angle exists.
–1.48 + pi n
–0.09 + pi n
Here is how I do these:
sin^-1 (.65)
I know from CAST that the sine is positive in quadrants I and II
so 2ndF sin .65 gave me .70758...
That is my quad I angle, so π - .70758 or 2.434 would be the quadrant II angle
of course adding/subtracting 2π will yield other answers:
my answer would be .71 + n(2π) and 2.434 + n(2π), where n is an integer
I don't see that answer but notice that to reach 2.434 they went in the negative directions, so
2.434 and -3.85 are co-terminal angles, so I guess the 2nd choice would be it.
Do the 2nd question in the same way, knowing that the tangent is negative in II and IV, also the period of the tangent function is π, so add nπ to your two answers.
To find the values of the inverse function in radians using a calculator, you can follow these steps:
1. Look for the inverse trigonometric function button on your calculator. It is usually denoted as "sin^(-1)" or "asin" for arcsine, and "tan^(-1)" or "atan" for arctangent.
2. Press the corresponding inverse trigonometric function button on your calculator.
3. Enter the value inside the parentheses, in this case, 0.65 for the sine inverse function and -0.09 for the tangent inverse function.
For the question:
sin^(-1)(0.65)
Using a calculator, you would press the sin^(-1) or asin button and enter 0.65. The calculator will give you the inverse sine in radians, which is approximately 0.71.
The correct answer is 0.71 + 2pi n and –0.71 + 2pi n, where n is an integer. This means that there are infinite solutions to this equation, and for every n (integer), you will get a different value that satisfies the equation.
For the question:
tan^(-1)(-0.09)
Using a calculator, you would press the tan^(-1) or atan button and enter -0.09. The calculator will give you the inverse tangent in radians, which is approximately -0.09.
The correct answer is -0.09 + pi n, where n is an integer. This means that there are infinite solutions to this equation, and for every n (integer), you will get a different value that satisfies the equation.
Keep in mind that when using a calculator, make sure it is set to the correct angle unit (degrees or radians) to obtain the desired results.