Engaging Mathematics Lesson on Trigonometry using PLT Skills

1. Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Real life cross/curricular links? Where are we in our journey? Which ones are you using? PLT Skills LESSON OBJECTIVES Always aim high! We are learning to: • Finding connections between different words. (Which PLT skills?) • Accurately use the cosine function to calculate missing sides and angles in right angled triangles. (Grade B) AUTHOR www.mistrymaths.co.uk

2. Which ones are you using? BRAIN IN GEAR Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills EXAMPLE DITDIONA can be rearranged to make ADDITION TASK Work out the following Mathematical anagrams: Opposite Adjacent Sine EXTENSION Develop your own Mathematical anagrams as above as a creative thinker.

3. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager STARTER PLT Skills TASK 86 18 Write 0.1 as a fraction Write 770000 in standard form Write as a % Find 15% of $420 1) 2) 4) 3) 99 20 $63 = 1 5 -4 90% 5.3 x 10 7.7 x 10 = = = 10 Write 0.00053 in standard form Value of: Expand and simplify: 7(x + 2) - 3(x - 5) Value of: 89 5) 6) 7) 8) 5 0 99x 86 x 100x 86.868686…… x 0.868686….. 2 = = = 4 = 7x + 14 – 3x + 15 1 = = = 32 = 4x + 29 EXTENSION . = . Factorise the following: Write 0.86 as a fraction x2 - 11x + 30 = ( )( ) x - 6 x - 5

4. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills TRIGONOMETRY Make sure your calculator is set to D or Deg not R or Rad INTRODUCTION – USING YOUR CALCULATOR Find the values, rounding the answers to 3s.f. where appropriate. (d) sin 0 5 4 (c) sin 90 (b) sin 26 (a) sin 54 8 7 0 0.809 0.438 1 = = = = (h) cos 0 (g) cos 90 (f) cos 26 (e) cos 54 1 0.588 0.899 0 = = = = (l) tan 0 (k) tan 89 (j) tan 26 (i) tan 54 0 1.38 0.488 57.3 = = = = (n) 6 cos 24 (o) 8 tan 44 (m) 4 sin 62 3.53 5.48 7.73 = = = (r) (p) (q) 5.26 = (s) sin (t) cos 8 9 5 -1 -1 sin 72 tan 18 cos 35 SHIFT sin SHIFT cos 51.3 9.77 27.7 34.8 = = = =

5. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills TRIGONOMETRY INTRODUCTION – LABELLING SIDES CORRECTLY This is opposite the right-angle. This is opposite the angle. Hypotenuse Opposite Adjacent This is next to the angle.

6. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills TRIGONOMETRY INTRODUCTION – LABELLING SIDES CORRECTLY Label the sides of the triangles below with opposite, adjacent and hypotenuse: (b) (d) (a) (c) A H O H H O A O A H A O O A A (f) (h) (e) (g) A O A H O H H O H

7. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills COSINE FUNCTION EXAMPLES (b) (a) H 16cm H 13cm O O 57° θ b A A 6cm Find the length of side b Find the angle θ SUBSTITUTE IN THE VALUES SUBSTITUTE IN THE VALUES LABEL THE SIDES LABEL THE SIDES WRITE DOWN THE FORMULA WRITE DOWN THE FORMULA 6 Adjacent Adjacent b cos θ = cos θ = cos θ = cos 57 = Hypotenuse Hypotenuse 13 16 -1 cos 6 θ = b = 16 x cos 57 13 b = 8.71cm(3s.f) θ = 62.5°(3s.f)

8. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills COSINE FUNCTION TASK (GRADE B) (a) (b) (c) (d) H A H H 3m A A H A Work out θ Work out θ Work out θ Work out θ (e) (f) (g) (h) A H H H A A H A Find the value of x Find the value of x Find the value of x Find the value of x

9. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills COSINE FUNCTION EXTENSION (GRADE B) 1) Angle θ has a cosine of . Calculate the missing lengths in these triangles. (a) (b) (c) (d) H A H H A A A H x2 4 x = 4 x3 6 x = 15 x6 12 x10 20 10 x2 x = 20 15 x3 50 x6 30 x10 2) Find the values of θ below: 3.27m x = 30 A (a) (b) (c) (d) H 0.56m H A H 6m 0.5m A A H

10. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills COSINE FUNCTION MINI-PLENARY – SPOT THE MISTAKE 2) 1) Find the length of x Find the angle θ H A H A

11. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager • LINK BACK TO OBJECTIVES • Accurately use the sine function to calculate missing sides and angles in right angled triangles. What grade are we working at? DISCOVERY PLT Skills

12. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills COSINE FUNCTION PLENARY ACTIVITY– PRACTICAL PROBLEM (GRADE B) A window cleaner has a ladder which is 9m long. The window cleaner leans it against a wall so that the foot of the ladder is 4m from the wall. What angle does the ladder make with the ground? θ 9m 4 θ = 9 θ = 63.6°(3s.f) Adjacent 4 cos θ = cos θ = 9 Hypotenuse 4m -1 cos

13. What grade are we working at? Where are we in our journey? What have you learnt? Draw your brain In your brain, write or draw everything you can remember about using the cosine function to calculate missing sides and angles in right angled triangles. It can be a skill or a reflection, or something else that might be prominent in your brain.

14. Team Worker Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen SELF ASSESSMENT Enterprise Skills Which ones are you using? Plenary Activity How well do you understand the task? . I fully understand I don’t understand I nearly understand www.mistrymaths.co.uk

15. Team Worker Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen SELF ASSESSMENT Enterprise Skills Which ones are you using? Plenary Activity WWW (What Went Well) EBI (Even Better If) On your post it notes… Think about how you can improve your work. www.mistrymaths.co.uk