Homework p.284-285 #3-99x3. #3 Determine the six trig functions of an angle whose terminal side contains.

Slides:



Advertisements
Similar presentations
Identify a unit circle and describe its relationship to real numbers
Advertisements

Evaluating Sine & Cosine and and Tangent (Section 7.4)
Section 5.3 Trigonometric Functions on the Unit Circle
7.4 Trigonometric Functions of General Angles
14.3 Trigonometric Functions. Objectives Find the values of the 6 trigonometric functions of an angle Find the trigonometric function values of a quadrantal.
2.3 Evaluating Trigonometric Functions for any Angle JMerrill, 2009.
Trigonometric Functions of Any Angles
H.Melikian/ Trigonometric Functions of Any Angles. The Unit Circle Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ 1. Use.
Copyright © Cengage Learning. All rights reserved. 4 Trigonometric Functions.
7-4 Evaluating Trigonometric Functions of Any Angle Evaluate trigonometric functions of any angle Use reference angles to evaluate trigonometric functions.
7.3 Trigonometric Functions of Angles. Angle in Standard Position Distance r from ( x, y ) to origin always (+) r ( x, y ) x y  y x.
EXAMPLE 1 Evaluate inverse trigonometric functions Evaluate the expression in both radians and degrees. a.cos –1 3 2 √ SOLUTION a. When 0 θ π or 0° 180°,
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.
Trigonometric Functions on the
Pre calculus Problem of the Day Homework: p odds, odds, odds On the unit circle name all indicated angles by their first positive.
Drill Calculate:.
Section 7-4 Evaluating and Graphing Sine and Cosine Objectives: To use the reference angles, calculators and tables and special angles to find the values.
4.4 Trigonometric Functions of any Angle Objective: Students will know how to evaluate trigonometric functions of any angle, and use reference angles to.
Finding Exact Values of Trig Ratios. Special Right Triangles
Section 5.3 Trigonometric Functions on the Unit Circle
1 Trigonometric Functions of Any Angle & Polar Coordinates Sections 8.1, 8.2, 8.3,
Trigonometric Functions of Any Angle & Polar Coordinates
13.2 – Define General Angles and Use Radian Measure.
Hosted by Mr. Guthrie Definitions Trig IdentitiesCoordinate Trig Trig Problems
2.1 Six Trig Functions for Right Triangles
Warm- Up 1. Find the sine, cosine and tangent of  A. 2. Find x. 12 x 51° A.
EXAMPLE 1 Evaluate trigonometric functions given a point
1 Chapter 4 Trigonometry Section 4 Trigonometric Functions of Any Angle to infinity and beyond... ! Math Analysis.
Right Triangle Trigonometry
Chapter 4 Trigonometric Functions Trig Functions of Any Angle Objectives:  Evaluate trigonometric functions of any angle.  Use reference angles.
14.2 The Circular Functions
THE UNIT CIRCLE Precalculus Trigonometric Functions
Trig/Precalculus Section 5.1 – 5.8 Pre-Test. For an angle in standard position, determine a coterminal angle that is between 0 o and 360 o. State the.
4.4 Trigonmetric functions of Any Angle. Objective Evaluate trigonometric functions of any angle Use reference angles to evaluate trig functions.
Finding Trigonometric Function Values using a Calculator Objective: Evaluate trigonometric functions using a calculator.
Chapter 4 Review of the Trigonometric Functions
Ac 7.4 (PC 4.4) - Do Now: Pre-Calc book. Hw: p (13, 16, 17, 25, 28, 34, 36, even) tomorrow: p.549 (60, 65, 69, 72, 77, 81, 88, 89, 92, 95,
Trigonometric Functions of Any Angle & Polar Coordinates
MATHPOWER TM 12, WESTERN EDITION Chapter 5 Trigonometric Equations.
14.4 REFERENCE ANGLES AND CALCULATOR TRIG. A reference angle is the smallest positive angle formed by the terminal side of the angle and the x- axis.
4.2 Trig Functions of Acute Angles. Trig Functions Adjacent Opposite Hypotenuse A B C Sine (θ) = sin = Cosine (θ ) = cos = Tangent (θ) = tan = Cosecant.
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.
Trigonometric Functions. Cosecant is reciprocal of sine. Secant is reciprocal of cosine. Cotangent is reciprocal of tangent.
4.3 Right Triangle Trigonometry Objective: In this lesson you will learn how to evaluate trigonometric functions of acute angles and how to use the fundamental.
Chapter 4 Trigonometric Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Trigonometric Functions of Any Angle.
14.1 The Unit Circle Part 2. When measuring in radians, we are finding a distance ____ the circle. This is called. What is the distance around a circle?
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.
Bell Work R Find the 6 trig functions for
Objective: Finding trigonometric functions of any angle. Warm up Make chart for special angles.
§5.3.  I can use the definitions of trigonometric functions of any angle.  I can use the signs of the trigonometric functions.  I can find the reference.
Trigonometric Functions of Any Angle
Trigonometric Functions: The Unit Circle
Do Now The terminal side of angle θ in standard position passes through the point (12, 16). Find the value of the six trigonometric functions of angle.
WARM UP Use special triangles to evaluate:.
All Six Trigonometric Functions
Chapter 1 Angles and The Trigonometric Functions
12-3 Trigonometric Functions of General Angles
Bell Ringer How many degrees is a radian?
Lesson 4.4 Trigonometric Functions of Any Angle
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Trigonometric Functions of Any Angle (Section 4-4)
4.4 Trig Functions of any Angle
Introduction to College Algebra & Trigonometry
Trigonometric Functions of Any Angle
Trigonometric Functions of Any Angle
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Solving for Exact Trigonometric Values Using the Unit Circle
4.4 Do Now: State the quadrant in which the angle lies.
Presentation transcript:

homework p #3-99x3

#3 Determine the six trig functions of an angle whose terminal side contains

#3 Determine the six trig functions of an angle whose terminal side contains

#6 Determine the six trig functions of an angle whose terminal side contains (8,15)

#6 Determine the six trig functions of an angle whose terminal side contains (8,15)

#9 Determine the six trig functions of an angle whose terminal side contains (-4,10)

#9 Determine the six trig functions of an angle whose terminal side contains (-4,10)

#12 Determine the six trig functions of an angle whose terminal side contains (3,-9)

#12 Determine the six trig functions of an angle whose terminal side contains (3,-9)

#15 State the quadrant in which lies. cot > 0 and cos > 0

#15 State the quadrant in which lies. cot > 0 and cos > 0

#18 Find the values of the six trigonometric functions of. Lies in Quadrant III

#18 Find the values of the six trigonometric functions of. Lies in Quadrant III

#21 Find the values of the six trigonometric functions of.

#21 Find the values of the six trigonometric functions of.

#24 Find the values of the six trigonometric functions of. is undefined.

#24 Find the values of the six trigonometric functions of. is undefined.

#27 The terminal side of lies on the line 2x-y=0 in Quadrant III. Give the six trig values by finding a point on the line.

#27 The terminal side of lies on the line 2x-y=0 in Quadrant III. Give the six trig values by finding a point on the line.

#30 Evaluate the trigonometric function of the quadrant angle.

#30 Evaluate the trigonometric function of the quadrant angle.

#33 Evaluate the trigonometric function of the quadrant angle.

#33 Evaluate the trigonometric function of the quadrant angle.

#36 Evaluate the trigonometric function of the quadrant angle.

#36 Evaluate the trigonometric function of the quadrant angle.

Reference Angle If θ is in standard position, then the reference angle θ′ associated with θ is the acute angle formed by the terminal side of θ and the x-axis. * Never make a reference angle to the y-axis!

#39 Find the reference anglefor the special angle Then sketch and in standard position.

#39 Find the reference anglefor the special angle Then sketch and in standard position.

#42 Find the reference anglefor the special angle Then sketch and in standard position.

#42 Find the reference anglefor the special angle Then sketch and in standard position.

#45 Find the reference anglefor the special angle Then sketch and in standard position.

#45 Find the reference anglefor the special angle Then sketch and in standard position.

#48 Find the reference anglefor the special angle Then sketch and in standard position.

#48 Find the reference anglefor the special angle Then sketch and in standard position.

#51 Find the reference anglefor the special angle Then sketch and in standard position.

#51 Find the reference anglefor the special angle Then sketch and in standard position.

#54 Evaluate the sine, cosine, and tangent of the angle without using a calculator.

#54 Evaluate the sine, cosine, and tangent of the angle without using a calculator.

#57 Evaluate the sine, cosine, and tangent of the angle without using a calculator.

#57 Evaluate the sine, cosine, and tangent of the angle without using a calculator.

#60 Evaluate the sine, cosine, and tangent of the angle without using a calculator.

#60 Evaluate the sine, cosine, and tangent of the angle without using a calculator.

#63 Evaluate the sine, cosine, and tangent of the angle without using a calculator.

#63 Evaluate the sine, cosine, and tangent of the angle without using a calculator.

#66 Evaluate the sine, cosine, and tangent of the angle without using a calculator.

#66 Evaluate the sine, cosine, and tangent of the angle without using a calculator.

#69 Find the indicated trig value in the specified quadrant.Quadrant III

#69 Find the indicated trig value in the specified quadrant.Quadrant III

#72 Find the indicated trig value in the specified quadrant.Quadrant III

#72 Find the indicated trig value in the specified quadrant.Quadrant III

#75 Use a calculator to evaluate the trig function. Round your answer to four decimal places.

#75 Use a calculator to evaluate the trig function. Round your answer to four decimal places.

#78 Use a calculator to evaluate the trig function. Round your answer to four decimal places.

#78 Use a calculator to evaluate the trig function. Round your answer to four decimal places.

#81 Use a calculator to evaluate the trig function. Round your answer to four decimal places.

#81 Use a calculator to evaluate the trig function. Round your answer to four decimal places.

#84 Use a calculator to evaluate the trig function. Round your answer to four decimal places.

#84 Use a calculator to evaluate the trig function. Round your answer to four decimal places.

#87 Use a calculator to evaluate the trig function. Round your answer to four decimal places.

#87 Use a calculator to evaluate the trig function. Round your answer to four decimal places.

#90 Use a calculator to evaluate the trig function. Round your answer to four decimal places.

#90 Use a calculator to evaluate the trig function. Round your answer to four decimal places.

#93 Find two solutions of the equation. Give your answers in degreesand in radians. Do not use a calculator. a)b)

#93 Find two solutions of the equation. Give your answers in degreesand in radians. Do not use a calculator. a)b)

#96 Find two solutions of the equation. Give your answers in degreesand in radians. Do not use a calculator. a)b)

#96 Find two solutions of the equation. Give your answers in degreesand in radians. Do not use a calculator. a)b)

#99 An airplane flying at an altitude of 6 miles is on a flight path that passes directly over an observer. If is the angle of elevation from the observer to the plane, find the distance from the observer to the plane when (a) (b) (c)

#99 An airplane flying at an altitude of 6 miles is on a flight path that passes directly over an observer. If is the angle of elevation from the observer to the plane, find the distance from the observer to the plane when (a) (b) (c)