7: Periodic Functions
- Page ID
- 145594
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In the previous chapter, the trigonometric functions were introduced as ratios of sides of a right triangle, and related to points on a circle. We noticed how the x and y values of the points did not change with repeated revolutions around the circle by finding coterminal angles. In this chapter, we will take a closer look at the important characteristics and applications of these types of functions, and begin solving equations involving them.
- 7.1: Sinusoidal Graphs
- In this section, we will work to sketch a graph of a rider’s height above the ground over time and express this height as a function of time.
- 7.2: Graphs of the Other Trig Functions
- In this section, we will explore the graphs of the other four trigonometric functions. We’ll begin with the tangent function.
- 7.3: Inverse Trigonometric Functions
- In previous sections, we have evaluated the trigonometric functions at various angles, but at times we need to know what angle would yield a specific sine, cosine, or tangent value. For this, we need inverse functions. Recall that for a one-to-one function, if f(a)=b, then an inverse function would satisfy f⁻¹(b)=a .
- 7.4: Solving Trigonometric Equations
- Previously, we learned sine and cosine values at commonly encountered angles. We can use these to solve sine and cosine equations involving these common angles.
- 7.5: Modeling with Trigonometric Functions
- Previously, we used trigonometry on a right triangle to solve for the sides of a triangle given one side and an additional angle. Using the inverse trig functions, we can solve for the angles of a right triangle given two sides.
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