1 / 12

Unit 3 Outcome 4

Higher. Unit 3 Outcome 4. The wave function and a cos α + a sin α. Lesson 1. Starter. Q1. Solution. 0. 2. ∫. ∫. x. dx +. x. dx. -2. 0. 2. ∫. 2. x. dx. 0. Answer D. Thursday, 02 October 2014. Higher. Unit 3 Outcome 4.

talia
Download Presentation

Unit 3 Outcome 4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Higher Unit 3 Outcome 4 The wave function and acos α + asin α Lesson 1 Starter Q1 Solution 0 2 ∫ ∫ x dx + x dx -2 0 2 ∫ 2 x dx 0 Answer D Thursday, 02 October 2014

  2. Higher Unit 3 Outcome 4 The wave function and acos α + asin α Example Write 4 cosx + 3sinx in the form K cos(x-α) 0 ≤ α≥ 360 Find K K = 42 + 32 4 cosx + 3 sinx = K cos(x - α) 0 ≤ α≥ 360 K = √ (42 + 32) = K [cosx cosα + sinxsin α] K = √ (16 + 9) K = √ 25 = K cosx cosα + K sinxsin α K = 5 = K cosαcosx + K sin αsinx Find α Reminder tan = sin α 4 cosx + 3 sinx cos α K sin α K cosα= 4 Cosα is pos tan α = cos α K sin α= 3 K sin α is pos tan α = 3 √ αis therefore in the 1st quadrant since cos and sin both positive √ S A √ 4 α = 36.9 √ 4 cosx + 3 sinx = K cos(x - α) T C 4 cosx + 3 sinx = 5 cos(x – 36.9) y = 5 cos (x – 36.9) Thursday, 02 October 2014

  3. Higher Unit 3 Outcome 4 The wave function and acos α + asin α Write the following in the form K cos (x - α) 0 ≤ α≥ 360 a) y = 10 cos(x – 53.13) a) 6 cosx + 8 sinx b) 5 cosx + 12 sinx b) y = 13 cos(x – 67.38) c) 8 cosx + 15 sinx c) y = 17 cos(x – 61.927) Thursday, 02 October 2014

  4. Higher Unit 3 Outcome 4 The wave function and acos α + asin α Wave Function Page 253 Exercise 1A Q2, Q3, Q4 Extension Wave Function Page 253 Exercise 1B Q1, Q2, Q4 Thursday, 02 October 2014

  5. Higher Unit 3 Outcome 4 The wave function and acos α + asin α Write the following in the form K cos (x - α) 0 ≤ α≥ 360 Exam Standard Question Thursday, 02 October 2014

  6. Express in the form Hint Maths4Scotland Higher Expand ksin(x - a): Equate coefficients: Square and add a is in 1st quadrant (sin and cos are both +) Dividing: Put together: Previous Next Quit Quit

  7. The diagram shows an incomplete graph of Find the coordinates of the maximum stationary point. Hint Maths4Scotland Higher Max for sine occurs Sine takes values between 1 and -1 Max value of sine function: Max value of function: 3 Coordinates of max s.p. Previous Next Quit Quit

  8. a) Express f (x) in the form b) Hence solve algebraically Hint Maths4Scotland Higher Expand kcos(x - a): Equate coefficients: Square and add a is in 1st quadrant (sin and cos are both + ) Dividing: Put together: Solve equation. Cosine +, so 1st & 4th quadrants Previous Next Quit Quit

  9. Hint Maths4Scotland Higher Solve the simultaneous equations where k > 0 and 0 x 360 Use tan A = sin A / cos A Divide Find acute angle Sine and cosine are both + in original equations Determine quadrant(s) Solution must be in 1st quadrant State solution Previous Next Quit Quit

  10. Hint Maths4Scotland Higher Solve the equation in the interval 0 x 360. Use Rcos(x - a): Equate coefficients: Square and add a is in 2nd quadrant (sin + and cos - ) Dividing: Put together: Solve equation. Cosine +, so 1st & 4th quadrants Previous Next Quit Quit

  11. Maths4Scotland Higher Table of exact values Return

  12. Higher Circle Unit 2 Outcome 4 Intersection of a Line and a circle Thursday, 02 October 2014

More Related