In this lesson students learn the names of the trigonometric ratios they have been using in the Right Triangle Table, and how to look them up on a calculator: Cosine is the ratio of the length of the adjacent leg to the length of the hypotenuse for a given acute angle in a right triangle. Sine is the ratio of the length of the opposite leg to the length of the hypotenuse. Tangent is the ratio of the length of the opposite leg to the length of the adjacent leg.

The decision to write the trigonometric ratios in the order “cosine, sine, tangent” is purposeful. Because cosine represents the -coordinate in the unit circle, while sine represents the -coordinate, tables in which cosine is in the first position correspond to the coordinates. This will not align with the SOHCAHTOA mnemonic, but it is not expected that students memorize these definitions. They can use their reference chart or the Right Triangle Table for reference at any time.

Trigonometric functions (which will be studied more generally in a future course) have inputs of angle measures and outputs of ratios. Right now, students know about angles measured only in degrees, so they are expected to interpret the cosine, sine, or tangent of an angle with the assumption that the angle is measured in degrees. People use the notation to mean a variety of things. Say angle  has a measure of 23 degrees. We might write or . We interpret to mean sine of the measure of angle . Students don’t need to consider this level of nuance, but be prepared to explain the different interpretations of trigonometric functions if it comes up.

It is important that students attend to precision (MP6) as they move from a table rounded to three decimal places to choosing how to use the very long decimal provided by a calculator. In this lesson students will discuss rounding and its effects in general.