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Trigonometry: Starter 1) Find the Sin Cos Tan functions on your calculator 2) Check your calculator is in degrees (DEG) or (D) Use mode to change DEG – RAD – GRAD Use your calculator to find… (answer to 3dp if needed) 3) Sin 30 = 4) Cos 30 = 5) Tan 45 = 6) Sin 60 = 7) Cos 60 = 8) Tan 135 = 9) Sin 28 = 10) Cos 77 = 11) Tan 90 = Trigonometry: Introduction A Hypotenuse length (h)= 30° Side length (a) = Calculate length( a ) length( h) Cos 30 = Trigonometry: Introduction B Hypotenuse length (h)= Side length (o) = 40° Calculate length( o ) length( h) Sin 40 = Trigonometry: Introduction C Side length (o) = 35° Side length (a) = Calculate length( o ) length( a ) Tan 35 = Trigonometry: Putting it together A 1 metre 25° We know that length(a ) Cos 25 length( h) So if (h) 1 then length(a ) Cos 25 x metres Or simply 4 metres 25° x metres x Cos 25 Trigonometry: Putting it together B x metres 1 metre We know that 34° length(o) Sin 34 length( h) So if (h) 1 then length(o) Sin 34 Or simply x metres 12 metres 34° x Sin 34 Trigonometry: Putting it together C We know that x metres 29° 1 metre x metres 42 metres 29° length(o) Tan 29 length(a ) So if (h) 1 then length(o) Tan 29 Or simply x Tan 29 Trigonometry: Rules Use Soh Cah Toa Hypotenuse (longest side) h (opposite side) o θ (adjacent side) a (o) (a) (o) Opposite Adjacent Opposite (h) Sin θ Hypotenuse (h) Cos θ Hypotenuse (a) Tan θ Adjacent Hypotenuse (longest side) Trigonometry: Steps 1) Label the triangle 2) Which two important sides? 3) Select the trig rule Soh Cah Toa 4) Write the rule triangle 5) Put in known values 6) Cover unknown value and solve 7) Working calculation 8) Answer sensible? 12 9) Units & rounding xm 66° 4.5 m h (opposite side) o θ (adjacent side) a cm x cm 20° Sin & Cos problems Beta pg 276 Ex 19.6 Trigonometry: Practice A Beta pg 277 Ex 19.7 Simple triangle problems Beta pg 278 Ex 19.6 Word & picture problems Tan problems Beta pg 281 Ex 19.9 Beta pg 281 Ex 19.10 Beta pg 282 Ex 19.11 Mixed problems Beta pg 282 Ex 19.12 Trigonometry: Practice B Sin & Cos problems Beta pg 285 Ex 20.2 Simple triangle problems Beta pg 285 Ex 20.3 Word & picture problems Mixed problems Beta pg 290 Ex 20.5 Word & picture problems Beta pg 292 Ex 20.6 Trigonometry: Finding the angle Hypotenuse (longest side) h (opposite side) θ o 6m (adjacent side) a θ˚ 4m (o) Opposite (a) Tan θ Adjacent 12 cm 16 cm θ° 1) Find the marked angle in the triangle. 400 m θ° 600 m 2) An aeroplane takes off and climbs in a straight line. If it flies 5000m through the air and climbs to a height of 1200m find the angle of climb. 3) A ship leaves port and sails north for 2.4 km then east for 5 km. Find the bearing the now is from the port Beta: pg 297 Ex 21.3 pg 298 Ex 21.4 Extension: pg 300 Ex 21.5