Chapter 12. Trigonometry

In this chapter, you explore the basic notions of trigonometry. You begin by reviewing the Pythagorean theorem. Exploring the standard triangle in this way puts you in a position to begin a preliminary inquiry into the notion of how you can arrive at a ratio between the lengths of the sides of a triangle from which you can know the sine of an angle. A further step involves exploring ways to measure angles. You can measure angles in degrees or radians. A radian can be viewed as an arc of a circle equal in length to the radius of the circle. Radians allow you to begin to explore trigonometric ratios and extend the sine ratio. These ratios consist of those involving the cosine, tangent, cotangent, secant, and cosecant. Toward familiarizing you with such notions, this chapter addresses the following topics, among others:

• How the slope of a linear graph relates to the side of a triangle

• Recognizing the standard form of a right triangle

• Transferring knowledge of a right triangle to a coordinate plane

• Interpreting a coordinate plane as a circle

• Explaining an angle using a unit circle

• Using a unit circle to explore the trigonometric ratios