Proofs Trigonometry Addition formulas KUS objectives BAT understand

Proofs

Trigonometry: Addition formulas • KUS objectives BAT understand where the addition formula come from and derive the double angle formulas BAT use the addition formulae to solve ‘show that’ problems BAT use the addition formulae to solve equations Starter:

WB 1 a: Show that Sin(A - B) ≡ Sin. ACos. B - Cos. ASin. B Sin(45 - 30) = Sin 45 Cos 30 – Cos 45 Sin 30

WB 1 b: Show that

5 A 3 4 Use Pythagoras’ to find the missing side (ignore negatives) Tan is positive in the range 180˚ - 270˚ 13 90 180 270 y= 360 Tanθ 5 B 12 Use Pythagoras’ to find the missing side (ignore negatives) Tan is negative in the range 90˚ - 180˚ 90 180 270 y= 360 Tanθ

Substitute in Tan. A and Tan. B Work out the Numerator and Denominator Leave, Change and Flip Simplify Although you could just type the whole thing into your calculator, you still need to show the stages for the workings marks…

Rewrite the sin and cos parts Multiply out the brackets Divide all by cosxcosy Simplify Subtract 3 tanxtany Subtract 2 tany Factorise the left side Divide by (2 – 3 tany)

• KUS objectives BAT understand where the addition formula come from and derive the double angle formulas BAT use the addition formulae to solve ‘show that’ problems BAT use the addition formulae to solve equations self-assess using: R / A / G ‘I am now able to ____. To improve I need to be able to ____’