By Adam Donnelly – Updated Aug 30, 2022

Calculating cosine with a calculator is far faster than using a trigonometry table. Cosine is a core concept in trigonometry, relating a non‑right angle to the ratio of its adjacent side over the hypotenuse in a right triangle.

Finding the Cosine of an Angle

1. Verify the calculator’s angle mode. On scientific models it’s shown on the display; on graphing units press Mode. Set to DEG for degrees (typical in geometry) or RAD for radians (used in advanced trig).
2. Press the Cos button – the screen should display cos(.
3. Enter the angle value. For example, type 45 for 45°.
4. Close the parenthesis by pressing ).
5. Hit Enter. The result appears as a decimal; 45° yields 0.7071.

Determining an Angle from a Cosine Ratio

1. Ensure the calculator is in the correct angle mode (DEG or RAD).
2. Press 2nd then Cos to access the inverse function (display shows cos⁻¹().
3. Enter the cosine ratio. Use a fraction if needed; for 1/2, type 1 ÷ 2.
4. Press Enter. The calculator returns the angle – 60° for a ratio of 0.5.

Quick Tips

• Angles for cosine must be less than 90° to satisfy the triangle angle sum.
• When entering a ratio, always provide a proper fraction; the hypotenuse is the denominator by definition.