1.2 The Trigonometric Ratios
Introduction:
In the 1.1 activity, we found that the ratio of the height divided by the base was the same across similar right triangles. We also discovered that the tangent of the angle at the origin was equal to this ratio. So it may not come as a surprise that we define the tangent of an angle theta (θ) as;
Like other functions we have encountered, tangent takes an angle as an input and outputs a ratio. There are two additional trig functions, sine and cosine, that follow similar rules.
The table shows us several ways to represent and remember each trig function. In particular the row reading "soh cah toa" is a common shorthand most students learn to quickly remember the ratio that belongs to each trig function.
It may be helpful to add the description of these three trig ratios to your notes.
Practice:
Practice setting up all three trig equations
Write the equation for the tangent of ∠A, then check your answer.
What about sine ∠A?
cosine of ∠A?
What if we switch to ∠C?
Changing the angle changes our equations
What will the sine equation if we use ∠C as our input?
What is the equation for cosine of ∠C?
tangent of ∠C?
Critical Thinking:
If we compare the equations in two practice problems, what could we say about their angles? What could we say about their ratios?