Trigonometry. This Instructable is originally intended for the ninth students at DIS, but anybody is welcome to learn about Trigonometry. In this Introduction, I will give a general overview of the topic of Trigonometry, tips on how to learn and study well, and then go into more detail. In Mathematics, it is always important to learn how to understand what you are doing, and why you are doing these steps as opposed to just memorizing it. Trigonometry is the study of triangles. In this instructable, I will start basic with naming the sides of the right triangles, the trigonometric functions, and then gradually increase the difficulty so that the reader can eventually see how to tackle these problems, and apply them to real world situations. I will also provide tips on how to study and learn this topic well. This tutorial requires you to already know some basic algebra and geometry.
Step 1: Formulas and Definitions
Formulas and Definitions
First Slide: Formulas - Sin = Opp/Hyp, Cos = Adj/Hypotenuse Tan = Opp/Adj
Note: x is the angle we are using to determine the opp, adj, or the hypotenuse. If it were another angle, then the opposite and adjacent would change. Tricks : Soh Cah Toa. You may have seen or heard of this many times. The S in Soh represents the Sine, while the o stands for opposite, and the h stands for hypotenuse.
Definitions: Hypotenuse - The longest side of a right triangle. Opposite to the 90° angle.
Opposite - The side opposite to the angle of reference.
Adjacent - The side that is next to the angle of reference that is not the hypotenuse.
Right Triangle - A triangle with one ninety degree angle.
Step 2: Practice Problems
Practice Problems Practice Problems
Second Slide: Steps
a) Please Identify the following sides of the triangles with the appropriate names involving opposite, adjacent, or the hypotenuse.
b) find the sin, cos, tan ratios of the given angle.
c) Solve for side x. (only for the top triangle)
d) use a calculator to find the numerical value of x. (top Triangle)
Tip: Use Pythagoras Theorem To solve for the third unknown side. Opp^2+Adj^2=Hyp^2. Then use algebra to solve for one of these sides.
Answers: Left Triangle- A) Hyp=5m, Adj=4m, Opp=3m B) SinC = ⅗, CosC = ⅘ TanC = ¾
Right Triangle- A) Hyp=x, Adj=unknown side, Opp=2,500.
B) Sin 23 = 2500/x, Cos 23 = unknown side/x, Tan 23 = 2500/unknown side.
C) 1. Sin 23 = 2500/x 2. x Sin 23 = 2500 3. x = 2500/Sin 23. d) Solve with a calculator. Do the same with cos and tan.
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Step 3: Finding the Sin and Cos of a Specific Angle
Finding the Sin and Cos of a Specific Angle Finding the Sin and Cos of a Specific Angle
Third Slide: Tricks on how to find the value of the sin, cos, tan of a specific angle.
Exp. Sin 30° = 1 (opposite)/2 (Hypotenuse) so it equals ½ = .5(calculator).
Cos 45° = 1/root 2 = .7071 (Calculator). You can use the pythagorean theorem to check that these are valid right triangles.
There are other examples of finding the ratio defining the trigonometric functions of specific angles. The first step is to find the values of the sides, and then divide them. For most angles, however, you will need a calculator. This step was made to help you understand what the strange numbers and decimals on your calculator mean whenever you find the sin, cos, or tan of an angle.
