Reference Angles and Trigonometric Functions of Any Angle Accelerated Pre-Calculus.

Slides:

Advertisements

Similar presentations

Section 5.3 Trigonometric Functions on the Unit Circle

Advertisements

Day 2 and Day 3 notes. 1.4 Definition of the Trigonometric Functions OBJ:  Evaluate trigonometric expressions involving quadrantal angles OBJ:  Find.

Sullivan Precalculus: Section 5.2 Trig Functions: Unit Circle

Trigonometric Functions of Any Angles

Trig Functions of Special Angles

H.Melikian/ Trigonometric Functions of Any Angles. The Unit Circle Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ 1. Use.

Trigonometry/Precalculus ( R )

Quiz 1) Find a coterminal angle to 2) Find a supplement to 3) What is the arcsin(.325) in both radians and degrees?

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 7.4 Trigonometric Functions of General Angles.

Trigonometry Day 3 Trig Functions of Any Angle Learning Target: 1.Given a point on the unit circle, I can find the six Trig ratios 2.Given one Trig ratio,

Copyright © 2009 Pearson Addison-Wesley Acute Angles and Right Triangle.

Lesson 4.4 Trigonometric Functions of Any Angle. Let  be an angle in standard position with (x, y) a point on the Terminal side of  and Trigonometric.

4.4 Trigonometric Functions of any Angle Objective: Students will know how to evaluate trigonometric functions of any angle, and use reference angles to.

OBJECTIVES: Evaluate trigonometric functions of any angle using reference angles. Trigonometric Functions of Non-Acute Angles.

Trigonometric Functions of General Angles Section 3.4.

Definition of Trigonometric Functions With trigonometric ratios of acute angles in triangles, we are limited to angles between 0 and 90 degrees. We now.

Section 5.3 Trigonometric Functions on the Unit Circle

Evaluating Trigonometric Functions Given a Point Use the given point on the terminal side of an angle θ in standard position. Then evaluate the 6 trigonometric.

Sullivan Algebra and Trigonometry: Section 7.2 Objectives of this Section Find the Value of Trigonometric Functions of Acute Angles Use the Fundamental.

7.2 Right Triangle Trigonometry. A triangle in which one angle is a right angle is called a right triangle. The side opposite the right angle is called.

30º 60º 1 45º 1 30º 60º 1 Do Now: Find the lengths of the legs of each triangle.

1 Chapter 4 Trigonometry Section 4 Trigonometric Functions of Any Angle to infinity and beyond... ! Math Analysis.

13-3 Radian Measure Today’s Objective: I can measure an angle in radians.

4.3 – Trigonometric Functions on the Unit Circle.

Chapter 4 Trigonometric Functions Trig Functions of Any Angle Objectives:  Evaluate trigonometric functions of any angle.  Use reference angles.

Warm-Up 8/26 Simplify the each radical expression

Sullivan Algebra and Trigonometry: Section 6.4 Trig Functions of General Angles Objectives of this Section Find the Exact Value of the Trigonometric Functions.

4.4 Trigonmetric functions of Any Angle. Objective Evaluate trigonometric functions of any angle Use reference angles to evaluate trig functions.

Pre-Calc Book Section 5.2 Trigonometric Functions of Real Numbers

Right Triangle Trigonometry

Notes Over Trigonometric Ratios SOHCAHTOA A B C.

Knight’s Charge: Precalculus 41 Right Triangle Trigonometry 1.

4.4 – Trigonometric Functions of any angle. What can we infer?? *We remember that from circles anyway right??? So for any angle….

Chapter 4 Pre-Calculus OHHS.

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.

4.4 Trigonometric Functions of Any Angle. Ex.Find the sine, cosine, and tangent of if (-3,4) is a point on the terminal side of. (-3,4) -3 4 ? =5.

Pre-AP Pre-Calculus Chapter 4, Section 3 Trigonometry Extended: The Circular Functions

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 7.4 Trigonometric Functions of General Angles.

Trigonometric Functions: Unit Circle Approach

Chapter 4 Trigonometric Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Trigonometric Functions of Any Angle.

Section 4.4 Trigonometric Functions of Any Angle.

4.4 Trig Functions of Any Angle Objectives: Evaluate trigonometric functions of any angle Use reference angles to evaluate trig functions.

5.2 Trigonometric Ratios in Right Triangles. A triangle in which one angle is a right angle is called a right triangle. The side opposite the right angle.

Trigonometric Functions of Any Angle

Copyright © 2017, 2013, 2009 Pearson Education, Inc.

Chapter 1 Angles and The Trigonometric Functions

12-3 Trigonometric Functions of General Angles

What are Reference Angles?

4.4 Section 4.4.

2.3 Evaluating Trigonometric Functions for any Angle

Unit Circle 1 (0,0) Center: Radius: -1.

Evaluating Trigonometric Functions

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Assorted Trig Topics Accelerated Math 3.

Do Now Find the measure of the supplement for each given angle.

Warm-up: Find the exact values of the other 5 trigonometric functions given sin= 3 2 with 0 <  < 90 CW: Right Triangle Trig.

4.3 – Trig Functions on the Unit Circle

12.3 Day 1 Notes Trigonometric Functions of General Angles

1.3 – Trigonometric Functions

How do we draw angles in standard position?

Standard Position, Coterminal and Reference Angles

Conversions, Angle Measures, Reference, Coterminal, Exact Values

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

α The terminal side of the angle here is r

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

5-3 The Unit Circle.

4.4 Do Now: State the quadrant in which the angle lies.

Presentation transcript:

Reference Angles and Trigonometric Functions of Any Angle Accelerated Pre-Calculus

Reference angle: The acute angle formed by the terminal side of and the horizontal axis.

Ex 1) Determine the reference angle for each of the following angles.

You Try! 1.Determine the reference angle for each of the following angles.

Ex 1) (3,-4) is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle.

Ex 2) (-2,-1) is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle.

You Try! The given point lies on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle. 1) (8,-6) 2) (4, 3)

Ex 3) Given, find the values of the other 5 trigonometric functions.

You Try: