notes over 6.3 evaluating trigonometric functions given a point use the given point on the terminal...

13

Notes Over 6.3 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 functions. 8 , 15 . 1 15 8 2 15 2 8 225 64 289 17 17 sin 8 17 cos 15 17 tan csc 8 17 sec 15 17 cot 8 15 15 8

Upload: daisy-stevenson

Post on 21-Jan-2016

216 views

Category:

Documents

0 download

Report

Download

Embed Size (px):

TRANSCRIPT

Page 1: Notes Over 6.3 Evaluating Trigonometric Functions Given a Point Use the given point on the terminal side of an angle θ in standard position. Then evaluate

Notes Over 6.3Evaluating Trigonometric Functions Given a PointUse the given point on the terminal side of an angle θ in standard position. Then evaluate the 6 trigonometric functions.

8,15 .1 15

8

215 28225 64

289 17

17sin

8

17

cos15

17

tan 8

15

csc8

17

sec15

17

cot 8

15

15

8

Page 2: Notes Over 6.3 Evaluating Trigonometric Functions Given a Point Use the given point on the terminal side of an angle θ in standard position. Then evaluate

Notes Over 6.3Evaluating Trigonometric Functions Given a PointUse the given point on the terminal side of an angle θ in standard position. Then evaluate the 6 trigonometric functions.

4,3 .2

3

4

23 249 1625 5

5sin 4

5

cos3

5

tan

4

3

csc4

5

sec3

5

cot 4

3

Page 3: Notes Over 6.3 Evaluating Trigonometric Functions Given a Point Use the given point on the terminal side of an angle θ in standard position. Then evaluate

Finding Reference AnglesFind the reference angle θ’ for each angle θ.

o210 .3

180210 o30

210

Notes Over 6.3

Page 4: Notes Over 6.3 Evaluating Trigonometric Functions Given a Point Use the given point on the terminal side of an angle θ in standard position. Then evaluate

Finding Reference AnglesFind the reference angle θ’ for each angle θ.

o300 .4

300360 o60

300

Notes Over 6.3

Page 5: Notes Over 6.3 Evaluating Trigonometric Functions Given a Point Use the given point on the terminal side of an angle θ in standard position. Then evaluate

Finding Reference AnglesFind the reference angle θ’ for each angle θ.

3

4 .5

3

4

3

3

4

Notes Over 6.3

Page 6: Notes Over 6.3 Evaluating Trigonometric Functions Given a Point Use the given point on the terminal side of an angle θ in standard position. Then evaluate

Finding Reference AnglesFind the reference angle θ’ for each angle θ.

4

5 .6

4

5

4

4

5

Notes Over 6.3

Page 7: Notes Over 6.3 Evaluating Trigonometric Functions Given a Point Use the given point on the terminal side of an angle θ in standard position. Then evaluate

Using Reference Angles to Evaluate Trigonometric Functions

Evaluate the function without using a calculator.

o225cos .7 180225

o45 225

All

o45cos2

2

Students

Take Calculus

Notes Over 6.3

Page 8: Notes Over 6.3 Evaluating Trigonometric Functions Given a Point Use the given point on the terminal side of an angle θ in standard position. Then evaluate

Using Reference Angles to Evaluate Trigonometric Functions

Evaluate the function without using a calculator.

o330 tan.8330360

o30330

All

o30tan3

3

Students

Take Calculus

Notes Over 6.3

Page 9: Notes Over 6.3 Evaluating Trigonometric Functions Given a Point Use the given point on the terminal side of an angle θ in standard position. Then evaluate

Using Reference Angles to Evaluate Trigonometric Functions

Evaluate the function without using a calculator.

3

4cot .9

3

4

3

3

4All

3cot

3

3

Students

Take Calculus

Notes Over 6.3

Page 10: Notes Over 6.3 Evaluating Trigonometric Functions Given a Point Use the given point on the terminal side of an angle θ in standard position. Then evaluate

Evaluating Inverse Trigonometric Functions

2

1sin .10 1 Where is sin a = 2

1

306

11o330

6

Evaluate the expression in both radians

and degrees . oo 3600 oo 3600

AllStudents

Take Calculus

30

6

7o210

6

Notes Over 6.3

Page 11: Notes Over 6.3 Evaluating Trigonometric Functions Given a Point Use the given point on the terminal side of an angle θ in standard position. Then evaluate

3

3 tan.11 1 Where is tan a =

3

3

306

11o330

6

Evaluating Inverse Trigonometric FunctionsEvaluate the expression in both radians

and degrees . oo 3600 oo 3600

Notes Over 6.3

AllStudents

Take Calculus

30

6

5 o150

6

Page 12: Notes Over 6.3 Evaluating Trigonometric Functions Given a Point Use the given point on the terminal side of an angle θ in standard position. Then evaluate

2

2cos .12 1 Where is cos a =

2

2

454

3 o135 4

Evaluating Inverse Trigonometric FunctionsEvaluate the expression in both radians

and degrees . oo 3600 oo 3600

Notes Over 6.3

AllStudents

Take Calculus

45

4

5 o225 4

Page 13: Notes Over 6.3 Evaluating Trigonometric Functions Given a Point Use the given point on the terminal side of an angle θ in standard position. Then evaluate

Notes Over 6.3

θ hypotenuse adjacent opposite There are 6 trig ratios that can be formed from the acute angle θ. Sine θ= sin θCosecant θ= csc θ Cosine θ= cos θSecant

pchs.psd202.orgpchs.psd202.org/documents/kmattern/1574183553.docx · Web viewUse the Pythagorean identity to find sin θ, cos θ, or tan θ, given the value of one of these functions

MATHEMATICAL ENGINEERING TECHNICAL REPORTS · polynomial matrix ΦA(θ) in variable θ deﬁned by ΦA(θ) = O A −A⊤ D(θ) where D(θ) is a block-diagonal matrix in which each

Trigonometry Lecture NotesChp6faculty.fiu.edu/~mcguckd/Trigonometry Lecture Notes_part2... · 2012-01-04 · sin csc 1 csc sin θ θ θ θ = = 1 cos s c 1 ... 15° as 60° - 45°

Θ Θ# n Θ# n Θ nranger.uta.edu/~weems/NOTES2320/sum18Z.pdf · _____ A. Construct a max-heap for the symbols in an alphabet B. Minimize the expected bits per symbol. C. Find the

matermiddlehigh.enschool.org · Web viewAug 25, 2020 · Use the Pythagorean identity to find sin θ, cos θ, or tan θ, given the value of one of these functions and the quadrant

EXAMPLE 1 Evaluate trigonometric functions given a point Let (–4, 3) be a point on the terminal side of an angle θ in standard position. Evaluate the six

· Modeling the 3-point correlation function 3 β" θ 12" θ 23" θ 31" r 1" r 2" r 3" π)θ 12+β" β+θ 31" r 1" r 2" r 3" z" x" Fig. 1.— Schematic for calculating the 3-point

13.1 Exploring Periodic Data Analyze the periodic function ... · Given: an angle in standard position with measure ϴ. The c osine of ϴ is the _____-coordinate of the point at which

T, · computation Statistical inference E 1 2 E...,, Best explanation P( )G θ P( ),E P( ), ... 1 θ E 2 θ Estimation θ Figure 1: Statistical ab duction The idea of statistical

Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Deflections of Beams - Katie's Exam Revisions...The maximum deflection occurs at the point where the slope . θ = dv/dx =0. Assuming θ=0 in the slope function: Finding x between 0

trigonometry introduction exam equations - MadAsMaths · 2020-04-10 · Solve the following trigonometric equation in the range given. 5sin 2cos 3 sin θ θ θ − = , 0 360° ≤

€¦ · Web view2020/08/04 · Use the Pythagorean identity to find sin θ, cos θ, or tan θ, given the value of one of these functions and the quadrant of θ

An Operational SSL HF System (MILCOM 2007) · ahP(θ) = (F1P(θ)ejϕ1(θ),.,FNCP(θ)ejϕNC(θ))T (7) (P representing the polarization type O or X) where {}Fn0(θ) and {}FnX (θ) represent

ME 301 METU MEmakted.org.tr/.../5.PositionAnalysisOfMechanisms2.pdf · 3 A Example 2 θ 12 A 0 Given: All the necessary C 4 link dimensions and the input crank angle θ 12 6 B 0 5

Systemanalyse Modellierung Bereich: modellgetriebenen ...€¦ · Modellierung) Gehalte wie . θ . w, θ. a, θ. matrix, oder Fließgeschwindigkeiten . sind • intensive . Variablen,

Physics 102: Lecture 21 Diffraction, Gratings, Resolving Power...Resolving Power To see two objects distinctly, need θ objects > θ min θ min θ objects Improve resolution by increasing

Chapter 9 Trigonometry - Macmillan Caribbean · 2017-06-29 · 2 4 cot θ – 4 cot θ – 3 = 0 (2 cot θ + 1) (2 cot θ – 3) = 0 . cot , cot 13 θ=− θ= 22. 2 θ=−2, θ= 3

Review exercise 2...Review exercise 2 1 a r=2 b For any point P on the line 3 cos 3 3sec cos θ r r θ θ = = = c In the triangle ONA π 3 cos 4 6 2 2 3 ON ON OA ON = = = = In the

Apresentação do PowerPoint · 2020-03-29 · Sistemas Mecânicos de Rotação. 2 2. dt d T k c J. θ − θ− ω= k T dt d c dt d J + + θ= θ θ. 2 2. J k. Freqüência angular

9.1 Circles and Spheres. Circle: ______________________________ ____________________________________ Given Point:______ Given distance:_______ Radius:

Γ Θ þ Θ ü ùΩ84.205.248.2/Books/Eidikh-Agwgh-PI/books/b_likeiou/l_b... · 2014-06-10 · Γ Θ þ Θ ü ùΩ Φ Γ ΄ þ Γ ü ÿ όμος 3ος. oΓio ii ù i Θ þ ü ù Ω

Given a right triangle with acute angle θ: θ

pnhs.psd202.orgpnhs.psd202.org/documents/amcnamar/1578947991.doc · Web viewUse the Pythagorean identity to find sin θ, cos θ, or tan θ, given the value of one of these functions

Estimating the number of pulses in a mass extinction · T given the extinctions θ 1…θ T. However, likelihood is viewed as a function of the extinctions, conditional on the data

Point-to-point shortest path problem (P2P): Given: Eﬃcient

Model Helicopter Control Using Body-mounted Vibro-tactile ... · heli cm θ θ ψθ (2) Definition of parameters in Equations (1) and (2) are given in . Table 1 The nonlinear governing

msbraggteaching.files.wordpress.com · Web view2015/02/06 · sin θ cos θ tan θ csc θ sec θ cot θ Recall: Cartesian Grid & C.A.S.T. Rule PRACTICE EXAMPLE 1 : State an equivalent

About Lock-In Amplifierscourses/p451/background_info/SRS_Lock-In... · Remember that the PSD output is proportional to Vsigcosθ, where θ = (θ sig − θ ref ). θ is the phase

User-Provided Connectivity Services A Basic Model and ...guerin/presentations/UPC_talk.pdf · • Utility function of user with roaming value θ U (θ) = F (θ,x)+ G (θ,m) − p

without the use of a calculator 1. a. θ 1 2...Solve sin(θ)=1 2. Find all solutions for 0!≤θ

MCPS Power Point given at seminar

Calculus flash cards - Weeblypatemath.weebly.com/uploads/5/2/5/8/52589185/calculus_flash_cards.pdfcos 2 π 1 tan θ (in terms of sine and/or cosine) sin cos θ θ cot θ (in terms

1 Overview of the course Forward Kinematics (given theta, find end- point) Inverse Kinematics (given end-point find theta) Dynamics (given input torques