Curriculum Design Mathematics -- Trigonometry

Curriculum Design Mathematics -- Trigonometry Grade Spiritual Principle: "And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...." -- First Kings, chapter 7, verses 23 and 26 This refers to the importance of studying exact measurements (see note) and utilizing mathematical principles to perform accurate calculations. Students will apply the basic principles of trigonometry to investigate and explain the characteristics of rational functions.

Students will apply these basic principles to understand why trigonometric measurement is necessary based on the limits of geometrical measurement. Students will understand basic principles of ratio, sine, cosine, and tangent. Students will be able to explain how trigonometry might be used in their daily lives. (Why is Trigonometry Important?, 2001). Suggested Activities and Experiences- 1. Introduction to Trigonometric Principles -- To find relevancy, students need to see why trigonometry was invented and what questions it can answer. In addition, there are different problem solving skills necessary when dealing with trigonometric functions.

Break students into groups so that there are at least 4 separate groups. Here is the problem: You are in a group which is to abseil down a rock face tomorrow. Your task is to estimate the height of the face. You have no measuring instruments. You need to determine the height to know how much rope to take. You cannot take excess rope as you are at the start of a four day exercise and you must not have extra weight with you.

Tomorrow morning you will walk the track which will take you to the top of the rock face. Questions on board to read: What information is available? How can height be measured? What units of measure can be used? How accurate would this method be? What problems may arise using some of the methods described? What might another way be of measuring height? Introduce principles of trigonometry and functions to show how this branch of mathematics can more accurately measure when it is not possible to use linear methods.

Activity -- Work through the rock face problem as a class using an overhead or projector. Ask for input on alternatives to this set of functions? Ask for, and brainstorm other measurements in which we can try our new method (e.g. measurement without a measurement tool). 2. Working on the concept of ratios. Using the measurement skills from Activity 1, students will calculate measurement and ratios to find patterns of sides of a triangle. This will develop the concepts of sine, cosine, and tangent ratios of angles.

Students should have a basic concept of ratio, be able to convert fractions to decimals up to three.