Reference Angles.

Slides:



Advertisements
Similar presentations
The Coordinate Plane By: Christine Berg Edited By:VTHamilton.
Advertisements

Co-ordinates & Rotations 2.
Goal: to rotate a figure around a central point
Learn to locate and graph points on the coordinate plane.
Vocabulary coordinate plane axes x-axis
The Coordinate Plane. A coordinate plane is formed when two number lines intersect. The coordinate plane is used to locate points. The two number lines.
REFLECTIONS, ROTATIONS AND TRANSLATIONS. Reflections.
Missing Angles Our learning objectives today To calculate missing angles on a straight line, around a point and in a triangle. To use a protractor to draw.
5/6/14 Obj: SWBAT apply properties of the Law of Sines and Cosines Bell Ringer: HW Requests: 13.3 WS In Class: 13.4 WS Homework: Complete 13.4 WS Education.
Find the reference angle
I. Vectors, straight lines, circles Point The lenght of a line segment Coordinates of the center of a line segment Vector Vector – origin at point A and.
Review: Special Right Triangles 30 o 60 o 45 o 13-2 Angles & the Unit Circle Day 1 Today’s Objective: I can work with angles in standard position.
Objective Graph and name ordered pairs (2-9).. Voc.  Coordinate system  Coordinate grid  Origin  X-axis  Y-axis  Quadrants  Ordered pairs  X-coordinate.
How do we draw angles in standard position?
360°450°630°720°090°180°270° 540° Where θ is given for Where are the solutions and how many solutions?
8-1 Standards 8a - Draw angles that are negative or are larger than 180° 8b - Find the quadrant and reference angles of a given angle in standard position.
Problem of the Day The angle formed by placing the vectors [4,0] and [a,b] tail-to-tail at the origin is 124 degrees. The length of [a,b] is 12. Find a.
VOCABULARY CHECK Prerequisite Skills 1. Draw a coordinate plane and label the x -axis, y - axis, origin, and Quadrant III. 2. In the inequality x ≥ 8,
CC8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non‐vertical line in the coordinate plane; derive.
Angles & the Unit Circle Day 1 Today’s Objective: I can work with angles in standard position.
The Coordinate Plane. We have worked with both horizontal and vertical number line s Horizontal
By, Mrs. Muller.  If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent
Problem The direction of the 75-lb forces may vary, but the angle between the forces is always 50 o. Determine the value of  for which the resultant.
Example Draw and reflect an isosceles triangle
Example Draw and reflect an isosceles triangle
Find the coordinates of A(3, 2) reflected across the x-axis.
Objective: Sequences of transformations.
Warm Up A figure has vertices A, B, and C. After a transformation, the image of the figure has vertices A′, B′, and C′. Draw the pre-image and the image.
Introduction to Trigonometry
Problem of the day 1.) Graph triangle XYZ: X (0, 4), Y (3, 0), and Z (3, 4) 2) Reflect XYZ over the x-axis 3) Translate X’Y’Z’ right 4, down 2 4) What.
Do-Now Solve the system of equations. (2, –20) and (–1, –2)
Jeopardy Final Jeopardy Translations Reflections Vocabulary Solve It
Graphing Linear Equations
I can draw rotations in the coordinate plane.
Weight Components on a Ramp
4.4 Section 4.4.
The Coordinate Plane By: Mr. Jay Mar Bolajo.
عناصر المثلثات المتشابهة Parts of Similar Triangles
The Coordinate Plane By: Christine Berg Edited By:VTHamilton.
Transformations Example Draw the line Draw 1 at , ,
What is the missing angle in the following triangles. #1. 17, 60, x #2
Clickers Bellwork A figure whose coordinates are : (2,2) (4,3) (6,7) & (5,0) is moved right 2 units and up 7. What are the figures new coordinates? Are.
Congruence and Transformations
Enlarge the figure by a scale factor of 2 from the origin.
Warmup: Which quadrant is indicated by “20° clockwise”? 
Section 2.1 Angles in Standard Position
What is the missing angle in the following triangles. #1. 17, 60, x #2
Graphing on the Coordinate Plane
Trigonometry Using Co-terminal and Reference Angles
©2009 G Dear – Not to be sold/Free to use
The Coordinate Plane By: Christine Berg Edited By:VTHamilton.
Plotting Points © T Madas.
Symmetry in Circles Isosceles triangles have two equal sides and two equal angles. e° f° b° 30° n° e = (180 – 30)°  2 m° a° 70° = 75° 110° a = 70°
Graphing on a Coordinate Plane
Triangle sum property.
Section 3.1 Radians and Angles in Standard Position
COORDINATE PLANE QUAD II QUAD I QUAD III QUAD IV Y-axis
Graphing on the Coordinate Plane
Translations, Reflections, & Rotations
Chapter Seven Construction and Scale Drawings
How do we draw angles in standard position?
Unit 9. Day 17..
11.3 Coordinate Plane Math 1.
Introduction to Orthographic Projections
Finding unknown angles of triangles
α The terminal side of the angle here is r
3.4 Circular Functions.
The Coordinate Plane #39.
The two number lines are called the axes.
Presentation transcript:

Reference Angles

The Reference Angle y The reference angle is the angle made in the triangle closest to the origin   ’ x ’

Find the reference angle y Find the reference angle for 288 Draw 288 angle Draw triangle back to x axis Find reference angle  x ’ ’ is what is left over from 360 360 – 288 = ’ = 72

Find the reference angle y Find the reference angle for 98 Draw 98 angle Draw triangle back to x axis Find reference angle  ’ x ’ is what is left over from 180 180 – 98 = ’ = 82

Find the reference angle y Find the reference angle for -55 Draw -55 angle Draw triangle back to x axis Find reference angle x ’  ’ is what is the same as measured from zero but the positive angle |-55| = ’ = 55