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Trigonometry

Use the law of cosines

Find the third side of a triangle when you know two sides and the angle between them.

Open in Trident

The law of cosines says c² = a² + b² − 2ab cos C, where C is the angle between sides a and b.

Example: a = 7, b = 9 and C = 60 degrees. Then c = √(49 + 81 − 63) = √67 = 8.185352772.

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.

  1. Switch to degree mode.

    mode▼▼▶enter2ndQUITmode

  2. Type √(7² + 9² − 2 × 7 × 9 × cos(60)). The square root is 2nd then x².

    2nd√x²7x²+9x²−2×7×9×cos60))enter

You should see8.185352772

Classic Graphing 84 key reference · Classic Graphing 84 manual

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.

  1. Type the same formula. The root is 2nd then x². Press the right arrow to step out of the root before enter.

    2nd√x²7x²+9x²−2×7×9×cos60)▶enter

  2. The exact answer is √67. Press the ◄► key for the decimal.

    ◄►

You should see8.185352772

Classic Scientific 30 key reference · Classic Scientific 30 manual

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.

  1. Press the square-root key, then type the inside of the root. Press the right arrow to step out before =.

    √7x²+9x²−2×7×9×cos60)▶=

  2. Press S⇔D to turn √67 into a decimal.

    S⇔D

You should see8.185352772

Natural Scientific 991 key reference · Natural Scientific 991 manual

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.

  1. Set degrees. The square-root is SHIFT then x².

    SHIFTSET UPMENU▼▼F2EXITSHIFT√x²7x²+9x²−2×7×9×cos60)▶EXE

  2. Press S⇔D for the decimal.

    S⇔D

You should see8.185352772

Natural Color Graphing key reference · Natural Color Graphing manual

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.

  1. Set degrees. The root is ctrl then x². It closes its own bracket, so only close the cos bracket yourself. Use ctrl enter for a decimal.

    menu9▼▶enterenterenterctrl√x²7x²+9x²−2×7×9×cos60)ctrl≈enter

You should see8.18535

Classic CAS key reference · Classic CAS manual

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.

  1. Square both sides and add them: 7 ENTER × 9 ENTER × +.

    7ENTER×9ENTER×+

  2. Work out 2ab cos C: 2 ENTER 7 × 9 × 60 COS ×.

    2ENTER7×9×60COS×

  3. Subtract, then press the square-root key.

    −√x

You should see8.1854

RPN Scientific 15 key reference · RPN Scientific 15 manual

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.

  1. Square both sides and add them: 7 ENTER × 9 ENTER × +.

    7ENTER×9ENTER×+

  2. Work out 2ab cos C: 2 ENTER 7 × 9 × 60 COS ×.

    2ENTER7×9×60COS×

  3. Subtract, then press the square-root key.

    −√x

You should seex: 8.1854

RPN Advanced 42 key reference · RPN Advanced 42 manual

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.

  1. Choose DEG. Then 7 and the left shift with the square-root key gives 49. Do the same for 9 and add.

    MODEF57◀x²√x9◀x²√x+

  2. Work out 2ab cos C: 2 ENTER 7 × 9 × 60 COS ×. Then subtract and take the square root.

    2ENTER7×9×60COS×−√x

You should see8.18535277187

RPN Power 48 key reference · RPN Power 48 manual

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