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Trigonometry

Check unit circle values

Find the exact values of sin, cos and tan at 30, 45 and 60 degrees.

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The angles 30, 45 and 60 degrees have exact answers with square roots: sin 60 = √3/2, cos 45 = √2/2 and tan 30 = √3/3.

Natural and Classic CAS calculators show these exact forms. A decimal-only calculator shows 0.8660254038 for sin 60, and you can check it against √3 ÷ 2.

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 degrees. Type sin(60).

    mode▼▼▶enter2ndQUITmodesin60)enter

  2. Check it against √3 ÷ 2 (the root is 2nd then x²).

    2nd√x²3)÷2enter

You should seesin(60) .8660254038 √(3)/2 .8660254038

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. This model starts in degrees. Type sin(60). The answer is exact.

    sin60)enter

You should see√3/2

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. The calculator starts in degrees. Type tan(30) and press =.

    tan30=

You should see√3/3

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. Press sin 60, cos 45 and tan 30, each followed by EXE.

    SHIFTSET UPMENU▼▼F2EXITsin60EXEcos45EXEtan30EXE

You should see√3/2 √2/2 √3/3

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. Press enter after each: sin(60), cos(45) and tan(30).

    menu9▼▶enterenterentersin60)entercos45)entertan30)enter

You should see√3/2 √2/2 √3/3

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. Key in 60 and press SIN.

    60SIN

  2. Check it against √3 ÷ 2: 3, the square-root key, 2, ÷.

    3√x2÷

You should see0.8660

RPN Scientific 15 key reference · RPN Scientific 15 manual

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