The height the end of the pump arm is above the ground is given by the equation H = 6 + 4Sin(πt) Oil Pump Problem where t = time in minutes And H is the.

Slides:

Advertisements

Similar presentations

13.6 – The Tangent Function. The Tangent Function Use a calculator to find the sine and cosine of each value of . Then calculate the ratio. 1. radians2.30.

Advertisements

4.5 Graphs of Sine and Cosine Functions

Aim: Graphs of y = sin x and y = cos x Course: Alg. 2 & Trig. Aim: What do the graphs of Trig functions look like? Do Now: You and a friend are the last.

Solving Equations = 4x – 5(6x – 10) -132 = 4x – 30x = -26x = -26x 7 = x.

Trigonometry Revision θ Hypotenuse Opposite Adjacent O SH A CH O TA.

A piston moves a distance of 12cm from top to bottom (starts at top) One complete piston movement takes 0.04 seconds. Piston Problem The equation for the.

X y 1 st Quadrant2 nd Quadrant 3 rd Quadrant4 th Quadrant 13.1 – The Rectangular Coordinate System origin x-axis y-axis.

2 step problems 5) Solve 0.5Cos(x) + 3 = 2.6 1) Solve 4Sin(x) = 2.6 2) Solve Cos(x) + 3 = ) Solve 2Tan(x) + 2 = ) Solve 2 + Sin(x) =

3.1 – Paired Data and The Rectangular Coordinate System

Terminal Arm Length and Special Case Triangles DAY 2.

Solving Trig Equations

Homework: Graphs & Trig Equations 1.State the amplitude, period & then sketch the graph of (a) y = 3 cos 5x + 10 ≤ x ≤ 90 (b)y = ½ sin 2x0 ≤ x ≤ 360.

Presentation Timer Select a time to count down from the clock above 60 min 45 min 30 min 20 min 15 min 10 min 5 min or less.

Presentation Timer Select a time to count down from the clock above 60 min 45 min 30 min 20 min 15 min 10 min 5 min or less.

Multiple Solution Problems

10.4A Polar Equations Rectangular: P (x, y) Polar: P (r,  )  r = radius (distance from origin)   = angle (radians)

C2: Trigonometrical Equations Learning Objective: to be able to solve simple trigonometrical equations in a given range.

Section 6 Part 1 Chapter 9. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives More About Parabolas and Their Applications Find.

Section 6.1 Notes Special Angles of the Unit Circle in degrees and radians.

Evaluating Inverse Trigonometric Functions

Section 1.1 Rectangular Coordinates; Graphing Utilities; Introduction to Graphing Equations.

The height the end of the pump arm is above the ground is given by the equation H = 6 + 4Sin(πt) Oil Pump Problem where t = time in minutes And H is the.

Section 1.5: Circles Definition circle: Set of points a fixed distance from a center point. Definition radius: Distance from center to any point.

Today in Precalculus Turn in graded worksheet Notes: Simulating circular motion – Ferris Wheels Homework.

Solving Trig Equations Starter CStarter C Starter C SolutionsStarter C Solutions Starter DStarter D Starter D SolutionsStarter D Solutions.

Pre-Calculus 1 st Semester Final Exam Review, Day 1 1. Write an equation to match the graph: 2. What is the domain of the function that represents the.

Simple Trigonometric Equations The sine graph below illustrates that there are many solutions to the trigonometric equation sin x = 0.5.

EXAMPLE 1 Graph a vertical translation Graph y = 2 sin 4x + 3. SOLUTION STEP 1 Identify the amplitude, period, horizontal shift, and vertical shift. Amplitude:

Higher Maths Revision Notes The Auxiliary Angle Get Started.

Do now Solve 4x 4 -65x (3, ∞) Write as an inequality Sketch Bound or unbound?

1.1 and 1.5 Rectangular Coordinates and Circles Every man dies, not every man really lives. -William Wallace.

Curves & circles. Write down a possible equation that this could represent y = 6 – 3x or y = -3x + 6.

Periodic Functions A periodic function is a function for which there is a repeating pattern of y-values over equal intervals of x. Each complete pattern.

Chapter 11 Trigonometric Functions 11.1 Trigonometric Ratios and General Angles 11.2 Trigonometric Ratios of Any Angles 11.3 Graphs of Sine, Cosine and.

3) 0.96) –0.99) –3/412) –0.6 15) 2 cycles; a = 2; Period = π 18) y = 4 sin (½x) 21) y = 1.5 sin (120x) 24) 27) 30) Period = π; y = 2.5 sin(2x) 33) Period.

#1 Find the quadrant in which lies.. #1 Find the quadrant in which lies.

Pre-Algebra Chapter 8 Review. Question #1 In which quadrant or on which axis does each point fall? a)(0,2) b)(-4,8) c)(7,1)

360° Trigonometric Graphs Higher Maths Trigonometric Functions1 y = sin x Half of the vertical height. Amplitude The horizontal width of one wave.

Further Trigonometry Graphs and equations. Determine the period, max and min of each graph Period = 360  b Amplitude = a Max = a + c Min = c – a Period.

Solving Trig Equations Multiple solutions for sin and cos Solving simple trig equations of form: sin k = c sin ak =c.

Parametric Equations ordered pairs (x, y) are based upon a third variable, t, called the parameterordered pairs (x, y) are based upon a third variable,

8.2 - Graphing Polar Equations

Trigonometric Graphs Period = 3600 Amplitude = 1

Piston Problem A piston moves a distance of 12cm from top to bottom (starts at top) One complete piston movement takes 0.04 seconds. The equation for the.

Trigonometric Functions Review

Algebra 2 Stat review 11.2, 11.3, 11.5.

Rate of change and tangent lines

CHAPTER 1 COMPLEX NUMBERS

Real-Life Scenarios 1. A rental car company charges a $35.00 fee plus an additional $0.15 per mile driven. A. Write a linear equation to model the cost.

Trig Functions and Acute Angles

Applications of Sinusoidal Functions

1 step solns A Home End 1) Solve Sin(x) = 0.24

9.2 Addition and Subtraction Identities

1 step solns A Home End 1) Solve Sin x = 0.24

Trig Review! Section 6.4 – 6.6, 7.5.

Radians Ratios Primary Reciprocal Scenarios

Unit 7B Review.

A graphing calculator is required for some problems or parts of problems 2000.

Section 2.3 – Systems of Inequalities Graphing Calculator Required

pencil, highlighter, calculator, red pen, assignment

pencil, red pen, highlighter, packet, notebook, calculator

Section 9.4 – Systems of Inequalities Graphing Calculator Required

Solving Trigonometric Equations by Algebraic Methods

Warmup The arms on a pair of tongs are each 8 inches long. They can open to an angle of up to 120°. What is the width of the largest object that can be.

Warm-Up 1) Sketch a graph of two lines that will never intersect.

( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , )

Rectangular Coordinates; Introduction to Graphing Equations

The Distance & Midpoint Formulas

Presentation transcript:

The height the end of the pump arm is above the ground is given by the equation H = 6 + 4Sin(πt) Oil Pump Problem where t = time in minutes And H is the vertical height in metres How long is the height of the pump arm above 7 metres from the ground in one complete cycle? Method A: unit circle Method B: unit circle Method C: graph Height ‘H’ Method D: accurate graph Notes

Oil Pump method A Solve 7 = 6 + 4Sin(A) 0.25 = Sin(A) A = A = π – Calculate Sin Home The height the end of the pump arm is above the ground is given by the equation H = 6 + 4Sin(πt) where t = time in minutes And H is the vertical height in metres 1 = 4Sin(A) π 0, 2π A TC S Positive Sin so Quadrant 1 & 2 = 0.92 min Quadrant 2 A = Let A = πt And t = A ÷ π t = ÷ π Solve 7 = 6 + 4Sin(πt) RADIANS! t = ÷ π = 0.08 min How long is the height of the pump arm above 7 metres from the ground in one complete cycle? Time = 0.92 – 0.08 = 0.84 min

Oil Pump method B Solve 7 = 6 + 4Sin(πt) 0.25 = Sin(πt) πt = πt = π – Calculate Sin The height the end of the pump arm is above the ground is given by the equation H = 6 + 4Sin(πt) where t = time in minutes And H is the vertical height in metres Height ‘H’ 1 = 4Sin(πt) π 0, 2π A TC S Positive Sin so Quadrant 1 & 2 2 nd time = 0.92 min (2dp) Quadrant 2 πt = RADIANS! 1 st time = ÷ π = 0.08 min How long is the height of the pump arm above 7 metres from the ground in one complete cycle? Time = 0.92 – 0.08 = 0.84 min Home

Oil Pump method C Solve 7 = 6 + 4Sin(πt) 0.25 = Sin(A) (A) = Sin The height the end of the pump arm is above the ground is given by the equation H = 6 + 4Sin(πt) where t = time in minutes And H is the vertical height in metres 1 = 4Sin(A) Sketch the graph A = Let A = πt Solve 7 = 6 + 4Sin(A) RADIANS! Or A = π – Or A = = 0.92 min And t = A ÷ π t = ÷ π t = ÷ π = 0.08 min How long is the height of the pump arm above 7 metres from the ground in one complete cycle? Time = 0.92 – 0.08 = 0.84 min Home

Oil Pump method D Solve 7 = 6 + 4Sin(πt) 0.25 = Sin(πt) t = 1 – 0.08 t = 0.92 min (πt) = Sin The height the end of the pump arm is above the ground is given by the equation H = 6 + 4Sin(πt) where t = time in minutes And H is the vertical height in metres Height ‘H’ 1 = 4Sin(πt) Sketch the graph πt = Length of 1 cycle is 2 π ÷ π = 2 Midpoint = 1 t = 0.08 min (2dp) RADIANS! How long is the height of the pump arm above 7 metres from the ground in one complete cycle? Time = 0.92 – 0.08 = 0.84 min Home

Oil Pump Notes Solve 7 = 6 + 4Sin(A) 0.25 = Sin(A) A = A = π – Calculate Sin The height the end of the pump arm is above the ground is given by the equation H = 6 + 4Sin(πt) where t = time in minutes And H is the vertical height in metres 1 = 4Sin(A) π 0, 2π A TC S Positive Sin so Quadrant 1 & 2 = 0.92 min Quadrant 2 A = Let A = πt And t = A ÷ π t = ÷ π Solve 7 = 6 + 4Sin(πt) RADIANS! t = ÷ π = 0.08 min How long is the height of the pump arm above 7 metres from the ground in one complete cycle? Time = 0.92 – 0.08 = 0.84 min Home