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

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

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STARTER Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXTENSION TASK 1)2) 3) 4) Write 0.7 as a fraction 5) Find 15% of $220 6) Write as a % Expand and simplify: 6(x + 1) - 3(x - 4) 7) 18 25 Write 0.79 as a fraction. Value of: 66 0 8) Value of: 3 2 100. Write 68000 in standard form Write 0.0081 in standard form = 7 10 = 6.8 x 10 4 = 72% = $33 Factorise the following: = 8.1 x 10 -3 = 6x + 6 – 3x + 12 = 3x + 18 = 1 = 1000 x 2 - 9x + 14 = ( )( ) x - 7x - 2 x 0.797979….. = 100x 79.797979…… = 99x 79 = x = 79 99

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

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

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

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θ Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? SINE FUNCTION EXAMPLES (a) (b) 4cm 11cm 42° 14cm b LABEL THE SIDES Find the angle θ H O A WRITE DOWN THE FORMULA sin θ = Opposite Hypotenuse SUBSTITUTE IN THE VALUES sin θ = 4 11 θ = sin 4 11 θ = 21.3°(3s.f) Find the length of side b LABEL THE SIDES H O A WRITE DOWN THE FORMULA sin θ = Opposite Hypotenuse SUBSTITUTE IN THE VALUES sin 42 = b 14 b = 14 x sin 42 b = 9.37cm(3s.f)

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

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x10 x3 Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? EXTENSION (GRADE B) (a) SINE FUNCTION (b)(c)(d) (a)(b)(c)(d) O H O H O H O H O H O H O H O H 1) Angle θ has a sine of. Calculate the missing lengths in these triangles. 2) Find the values of θ below: 10 x2 6 x = 6 15 x3 9 x = 15 50 x10 30 x = 30 x6 30 x6 18 x = 30 5m 0.5m 0.12m 6.5m 64.5

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

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DISCOVERY Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills 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?

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7 Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? SINE FUNCTION PLENARY ACTIVITY– PRACTICAL PROBLEM (GRADE B) A window cleaner has a ladder which is 7m long. The window cleaner leans it against a wall so that the foot of the ladder is 3m from the wall. What angle does the ladder make with the wall? 7m 3m θ sin θ = Opposite Hypotenuse sin θ = 3 7 θ = sin 3 θ = 25.4°(3s.f)

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Draw your brain What have you learnt? In your brain, write or draw everything you can remember about using the sine 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. What grade are we working at? Where are we in our journey?

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

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

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