What is so surprising? The sine and cosine functions have ranges that span the closed interval [-1,1]. As to the tangent function, its range is the the whole real line.
This being said, you should keep in mind that there are three angle units: the degree, the radian, and the grad.
When you want to calculate the sine, cosine, or tangent of a number, that number is not just a number. It is an angle, and as an angle it has a unit.
For this reason a calculator generally has two angle units defined (degree and radian), and possibly the grad. BEFORE calculating any trigonometric function you must
ascertain that the angle is in the correct unit.
Clearly, in the problem you are trying to solve angle values are given in degrees, but your calculator is configured to interpret angles values in radians.
To set the default angle unit to degree press [MODE] , then press down arrow twice to reach the line (radian, degree). Highlight the word degree and press [ENTER] to set the default angle unit to degree.
Unfortunately the TI 8xPLUS family of calculators does not have a status bar on screen to remind you of the modes, and if you do not remember to check the current unit you get errors (at least unexpected results).
However, there is a way to avoid the errors and that is to enter the unit explicitly after the angle value. To do that you press [2nd][APPS] to open the (ANGLE) menu list. Try it.
- First item in list is the degree symbol, a raised 0
- 2nd is the minute, an apostrophe
- 3rd is radian, a raised r
By selecting the degree symbol and pressing [ENTER}, that symbol echoes on the screen just after the angle value. Closing the right parenthesis of the trigonometric function and pressing [ENTER] will give you the result in the correct unit of your choice. This can be done regardless of the default unit the calculator is configured for.
