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Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker 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 sine function to calculate missing sides and angles in right angled triangles. (Grade B) Where are we in our journey? AUTHOR www.mistrymaths.co.uk Real life cross/curricular links? Creative Thinker PLT Skills Effective Participator Independent Enquirer Reflective Learner BRAIN IN GEAR Self Manager Team Worker Which ones are you using? EXAMPLE DITDIONA can be rearranged to make ADDITION TASK Work out the following Mathematical anagrams: NEVERIS Inverse TAHET Theta TOPHEYESUN Hypotenuse EXTENSION Develop your own Mathematical anagrams as above as a creative thinker. Creative Thinker Effective Participator PLT Skills Independent Enquirer Reflective Learner STARTER Self Manager Team Worker Which ones are you using? TASK 1)Write 0.7 as 2) Write 68000 in 3) Write a fraction 7 = 10 = 5)Write 0.0081 in standard -3form = 8.1 x 10 EXTENSION .. standard form 4 6.8 x 10 = 18 25 4) Find 15% of $220 as a % 72% = $33 6) Expand and simplify: 7) Value of: 8) Value of: = = 6(x + 1) - 3(x - 4) 6x + 6 – 3x + 12 3x + 18 3 2 0 = 66 1 = 100 1000 Write 0.79 as a fraction Factorise the following: x = 0.797979….. 100x = 79.797979…… 99x = 79 x2 - 9x + 14 = ( x - 7 )( x - 2 ) x = 79 99 Creative Thinker PLT Skills Effective Participator Independent Enquirer Reflective Learner TRIGONOMETRY Self Manager Team Worker Which ones are you using? 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. (a) sin 54 (b) sin 26 (c) sin 90 (d) sin 0 = 0 = 0.809 = 0.438 = 1 (e) cos 54 (f) cos 26 (g) cos 90 (h) cos 0 = 1 = 0.588 = 0.899 = 0 (i) tan 54 (j) tan 26 (k) tan 89 (l) tan 0 = 0 = 1.38 = 0.488 = 57.3 5 (p) (n) 6 cos 24 (o) 8 tan 44 (m) 4 sin 62 sin 72 = 3.53 = 5.48 = 7.73 = 5.26 5 4 (q) 8 (r) 9 (s) sin-1 7 (t) cos-1 8 cos 35 = 9.77 tan 18 = 27.7 SHIFT sin = 34.8 SHIFT cos = 51.3 Creative Thinker PLT Skills Effective Participator Independent Enquirer Reflective Learner TRIGONOMETRY Self Manager Which ones are you using? INTRODUCTION – LABELLING SIDES CORRECTLY This is opposite the angle. Team Worker This is opposite the right-angle. This is next to the angle. Creative Thinker Effective Participator PLT Skills Independent Enquirer Reflective Learner Self Manager Team Worker Which ones are you using? 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 O A A A (e) O (f) A H A O H O A (g) H (h) A H O O H Creative Thinker Effective Participator PLT Skills Independent Enquirer Reflective Learner SINE FUNCTION EXAMPLES (a) Which ones are you using? H θ A Find the angle θ SUBSTITUTE IN THE VALUES LABEL SIDES WRITE DOWNTHE THE FORMULA Opposite Hypotenuse 4 sin θ = 11 4 sin θ = -1 Team Worker (b) 11cm H O 4cm Self Manager θ = sin 11 θ = 21.3°(3s.f) 14cm b O 42° A Find the length of side b SUBSTITUTE IN THE VALUES LABEL SIDES WRITE DOWNTHE THE FORMULA Opposite Hypotenuse b sin 42 = 14 sin θ = b = 14 x sin 42 b = 9.37cm(3s.f) Creative Thinker Effective Participator PLT Skills Independent Enquirer Reflective Learner Self Manager Team Worker Which ones are you using? SINE FUNCTION TASK (GRADE B) (a) (b) H O O Work out θ (f) H H O Work out θ (g) H (d) H O Work out θ (e) (c) H Work out θ O (h) H O Find the value of x O Find the value of x H Find the value of x O Find the value of x Creative Thinker Effective Participator PLT Skills Independent Enquirer Reflective Learner SINE FUNCTION Self Manager Team Worker Which ones are you using? EXTENSION (GRADE B) 1) Angle θ has a sine of . Calculate the missing lengths in these triangles. (a) (b) (c) (d) H H O O H O x2 6 x2 10 x=6 2) Find the values of θ below: (a) (b) H O O H x3 9 x3 15 x = 15 H x10 30 x10 50 x x6 18 x6 30 = 30 x = 30 (d) H O (c) 0.12m 5m 0.5m O H O 6.5m 64.5 Creative Thinker Effective Participator PLT Skills Independent Enquirer Reflective Learner SINE FUNCTION Self Manager Team Worker Which ones are you using? MINI-PLENARY – SPOT THE MISTAKE 1) Find the angle θ 2) Find the length of x H O H O Creative Thinker PLT Skills Effective Participator Independent Enquirer Reflective Learner DISCOVERY Self Manager Team Worker Which ones are you using? 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? Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker Which ones are you using? PLT Skills 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? θ 7m Opposite Hypotenuse sin θ = 3 7 3 sin θ = θ = sin -1 7 θ = 25.4°(3s.f) 3m What have you learnt? Draw your brain 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. Where are we in our journey? What grade are we working at? Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Enterprise Skills SELF ASSESSMENT Which ones are you using? Plenary Activity How well do you understand the task? . I don’t understand I nearly understand www.mistrymaths.co.uk I fully understand Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Enterprise Skills SELF ASSESSMENT 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