Presentation on theme: "1 7.2 Right Triangle Trigonometry In this section, we will study the following topics: Evaluating trig functions of acute angles using right triangles."— Presentation transcript:
1 7.2 Right Triangle Trigonometry In this section, we will study the following topics: Evaluating trig functions of acute angles using right triangles Use Fundamental Identities Use the Complimentary Angle Theorem
2 Take a look at the right triangle, with an acute angle, , in the figure below. Notice how the three sides are labeled in reference to . The sides of a right triangle Side adjacent to Side opposite Hypotenuse We will be reviewing special ratios of these sides of the right triangle, with respect to angle, . These ratios are better known as our six basic trig functions.
3 Six Trigonometric Functions
5 To remember the definitions of Sine, Cosine and Tangent, we use the acronym : “SOH CAH TOA” Definitions of the Six Trigonometric Functions
Find the value of each of the six trigonometric functions of the angle .
7 Find the exact value of the six trig functions of : Example 5 9 Hint: First find the length of the hypotenuse using the Pythagorean Theorem.
8 Example (cont) 5 9 So the six trig functions are:
9 Given that is an acute angle and, find the exact value of the six trig functions of . Example
This is known as a Pythagorean Identity.
13 Divide each side by cos 2 to derive 2 nd Pythagorean Identity.
14 Divide each side by sin 2 to derive 3 rd Pythagorean Identity.