Find an angle from a ratio
Use the inverse trig functions (sin⁻¹, cos⁻¹, tan⁻¹) to turn a ratio back into an angle.
If you know the ratio of two sides, the inverse function gives the angle. The example finds the angle whose tangent is 2. In degrees it is 63.43494882.
The inverse keys are the second function printed above sin, cos and tan.
Classic Graphing 84
Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.
Switch to degree mode.
mode▼▼▶enter2ndQUITmodePress 2nd then tan to get tan⁻¹, type 2, close the bracket and press enter.
2ndtan⁻¹tan2)enter
You should see63.43494882
Classic Scientific 30
Start on the main screen: Press 2nd then mode (QUIT) to leave any menu or screen and return to the calculation screen.
This model starts in degrees. Press 2nd then tan for tan⁻¹, type 2, close the bracket and press enter.
2ndtan⁻¹tan2)enter
You should see63.43494882
Natural Scientific 991
Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.
This model starts in degrees. Press SHIFT then tan, type 2 and press =.
SHIFTtan⁻¹tan2)=
You should see63.43494882
Natural Color Graphing
Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.
Set the angle unit to degrees.
SHIFTSET UPMENU▼▼F2EXITPress SHIFT then tan, type 2 and press EXE.
SHIFTtan⁻¹tan2EXE
You should see63.43494882
Classic CAS
Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.
Set degrees in Settings.
menu9▼▶enterenterenterPress ctrl then tan for tan⁻¹, type 2, close the bracket and press ctrl enter for a decimal.
ctrltan⁻¹tan2)ctrl≈enter
You should see63.4349
RPN Scientific 15
Start on the main screen: There is no menu to leave. Press the back arrow to clear a number you are typing, or CLx (g then back arrow) to clear the X register.
This model starts in degrees. Key in 2, then press g and TAN for the inverse tangent.
2gTAN⁻¹TAN
You should see63.4349
RPN Advanced 42
Start on the main screen: Press EXIT (once or twice) to close any menu and return to the plain stack view of Y and X.
Key in 2 and press shift then TAN (ATAN).
2⇧ATANTAN
You should seex: 63.4349
RPN Power 48
Start on the main screen: Press ON to cancel what you are typing, then use the stack view. Open the MODE or VAR menu any time; the stack is always shown above the menu row.
Pick DEG on the MODE menu.
MODEF5Key in 2, then press the left shift and TAN for the inverse tangent.
2◀ATANTAN
You should see63.4349488229
Tips
- sin⁻¹ and cos⁻¹ only accept values from -1 to 1. Anything else gives a domain error.
- The inverse key is not a power. sin⁻¹(x) is not the same as 1 ÷ sin(x). For that, see the reciprocal functions guide.
Related guides
- Find sine, cosine and tangentGet sin, cos or tan of an angle, here sin 50, cos 50 and tan 50 in degrees.
- Solve a right triangleFind a missing side from the hypotenuse and an angle, and a missing angle from two sides.
- Secant, cosecant and cotangentGet sec, csc and cot by taking the reciprocal of cos, sin and tan.