Download presentation

Presentation is loading. Please wait.

1
Right Triangle Trigonometry Digital Lesson

2
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 The six trigonometric functions of a right triangle, with an acute angle , are defined by ratios of two sides of the triangle. The sides of the right triangle are: the side opposite the acute angle , the side adjacent to the acute angle , and the hypotenuse of the right triangle. The trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. opp adj hyp θ Trigonometric Functions sin = cos = tan = csc = sec = cot = opp hyp adj hyp adj opp adj

3
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 3

4
4

5
5

6
6 60 ○ Consider an equilateral triangle with each side of length 2. The perpendicular bisector of the base bisects the opposite angle. The three sides are equal, so the angles are equal; each is 60 . Geometry of the 30-60-90 triangle 22 2 11 30 ○ Use the Pythagorean Theorem to find the length of the altitude,. Geometry of the 30-60-90 Triangle

7
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 7

8
8 Calculate the trigonometric functions for a 60 angle. 1 2 60 ○ Example: Trig Functions for 60 csc 60 = = = opp hyp sec 60 = = = 2 adj hyp cos 60 = = hyp adj tan 60 = = = adj opp cot 60 = = = opp adj sin 60 = =

9
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 9 Trigonometric Identities are trigonometric equations that hold for all values of the variables. Example: sin = cos(90 ), for 0 < < 90 Note that and 90 are complementary angles. Side a is opposite θ and also adjacent to 90 ○ – θ. a hyp b θ 90 ○ – θ sin = and cos (90 ) =. So, sin = cos (90 ). Example: Using Trigonometric Identities

10
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 10 Fundamental Trigonometric Identities for 0 < < 90 . Cofunction Identities sin = cos(90 ) cos = sin(90 ) tan = cot(90 ) cot = tan(90 ) sec = csc(90 ) csc = sec(90 ) Reciprocal Identities sin = 1/csc cos = 1/sec tan = 1/cot cot = 1/tan sec = 1/cos csc = 1/sin Quotient Identities tan = sin /cos cot = cos /sin Pythagorean Identities sin 2 + cos 2 = 1 tan 2 + 1 = sec 2 cot 2 + 1 = csc 2 Fundamental Trigonometric Identities for

11
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 11

12
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 12 Example: Given sec = 4, find the values of the other five trigonometric functions of . Use the Pythagorean Theorem to solve for the third side of the triangle. tan = = cot =sin = csc = = cos = sec = = 4 θ 4 1 Draw a right triangle with an angle such that 4 = sec = =. adj hyp Example: Given 1 Trig Function, Find Other Functions

13
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 13

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google