Download presentation

Presentation is loading. Please wait.

Published byJacob Morse Modified over 4 years ago

1
Trigonometry Math is beautiful. Is it? Well, if its not nice, than its damn sure of a very B.I.G. *HELP*.

2
Trigonometry Rotation of any object in an orthogonal system is done very easy using trigonometry. Trigonometry is all about the circle having a radius of 1 unit in length. We will rapidly show the theory behind using this circle.

3
Trigonometry The formula we will determine is useful in rotating a point x by a number of degrees/ radians from its initial position around a center O. You need to know the initial coordinates of x and the angle by which the point must be rotated around O.

4
Trigonometry r O r = 1 x(a, b) A a = r * cos(A) b = r * sin(A) B x(c, d) c = r * cos(A + B) d = r * sin(A + B) Known values r, a, b, B Values to be found c, d

5
Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) r * cos(A + B) = r * (cos(A)cos(B) - sin(A)sin(B)) = = r * cos(A)cos(B) – r * sin(A)sin(B) r * sin(A + B) = r * (sin(A)cos(B) + cos(A)sin(B)) = = r * sin(A)cos(B) + r * cos(A)sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

6
Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) r * cos(A + B) = r * cos(A)cos(B) – r * sin(A)sin(B) r * sin(A + B) = r * sin(A)cos(B) + r * cos(A)sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

7
Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) r * cos(A + B) = r * cos(A)cos(B) – r * sin(A)sin(B) r * sin(A + B) = r * sin(A)cos(B) + r * cos(A)sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

8
Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) r * cos(A + B) = a * cos(B) – r * sin(A)sin(B) r * sin(A + B) = r * sin(A)cos(B) + a * sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

9
Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) r * cos(A + B) = a * cos(B) – r * sin(A)sin(B) r * sin(A + B) = r * sin(A)cos(B) + a * sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

10
Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) r * cos(A + B) = a * cos(B) – b * sin(B) r * sin(A + B) = b * cos(B) + a * sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

11
Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) r * cos(A + B) = a * cos(B) – b * sin(B) r * sin(A + B) = b * cos(B) + a * sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

12
Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) c = a * cos(B) – b * sin(B) r * sin(A + B) = b * cos(B) + a * sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

13
Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) c = a * cos(B) – b * sin(B) r * sin(A + B) = b * cos(B) + a * sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

14
Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) c = a * cos(B) – b * sin(B) d = b * cos(B) + a * sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

15
Trigonometry cos(A + B) = cos(A)cos(B) - sin(A)sin(B) sin(A + B) = sin(A)cos(B) + cos(A)sin(B) c = a * cos(B) – b * sin(B) d = b * cos(B) + a * sin(B) a = r * cos(A) ; b = r * sin(A) ; r = 1 c = r * cos(A + B) d = r * sin(A + B)

16
Trigonometry c = a * cos(B) – b * sin(B) d = b * cos(B) + a * sin(B) (c, d) pair represents the coordinates of x that is actually x after the rotation

Similar presentations

OK

Quiz 13-2 1. 2. 3. Convert to degrees Convert to radians Arc length = Arc length = inches Radius = Radius = 6 inches What is the angle measure (in radians)?

Quiz 13-2 1. 2. 3. Convert to degrees Convert to radians Arc length = Arc length = inches Radius = Radius = 6 inches What is the angle measure (in radians)?

© 2018 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