1. Trig Graphs
And equations
Revision

2. sin 𝜃 =− sin (−𝜃) sin 𝜃 = sin (180−𝜃) 𝑐𝑜𝑠 𝜃 = 𝑐𝑜s (−𝜃)
Radians
These are the Trigonometric graphs, what are their properties ?… y
y = sinθ
sin 𝜃 =− sin (−𝜃)
sin 𝜃 = sin (180−𝜃)
cos 𝜃 = cos (360−𝜃)
𝑐𝑜𝑠 𝜃 = 𝑐𝑜s (−𝜃)
tan 𝜃 =− tan (−𝜃)
tan 𝜃 = tan (𝜃+180)
Properties of the graphs
Can you put them in words? 1 θ
-360º
-270º
-180º
-90º
90º
180º
270º
360º -1 y
y = cosθ 1 θ
-360º
-270º
-180º
-90º
90º
180º
270º
360º -1
y = tanθ 1 θ
-360º
-270º
-180º
-90º
90º
180º
270º
360º -1

3. 𝐴𝑟𝑒𝑎= 1 2 𝑎𝑏 sin 𝐶 𝑎 2 = 𝑏 2 + 𝑐 2 −2𝑏𝑐 cos 𝐴 Trig Triangles
Can you write three formulas for Trig with triangles (any triangles)
Trig Triangles
𝑎 2 = 𝑏 2 + 𝑐 2 −2𝑏𝑐 cos 𝐴
𝐴𝑟𝑒𝑎= 1 2 𝑎𝑏 sin 𝐶
Trig Identities
Can you write two useful Trig identities

4. 9. Solve, for -180 ≤ x < 180, 2 sin (𝑥+30) = cos (𝑥+30) ⁡
Give your answers to one decimal place.
(Solutions based entirely on graphical or numerical methods are not acceptable.)
(5)

5. 9. Solve, for -180 ≤ x < 180, 2 sin (𝑥+30) = cos (𝑥+30) ⁡
Give your answers to one decimal place.
(Solutions based entirely on graphical or numerical methods are not acceptable.)
(5)
SOLUTION and MARKSCHEME
Rearrange to tan 𝑥+30 = B1
Use arctan 𝒕𝒂𝒏 −𝟏 1 2 =26.565… or 𝑥+30=26.565… M1
Solves for one answer or 𝑥=26.565−30=−𝟑.𝟒° A1
Makes list / set answers 𝑥+30=− , , , … M1
Solves to find other answer in range 𝑥= −30=𝟏𝟕𝟔.𝟔° A1

6. 9. Solve, for 360 ≤ x < 540, 12 sin2 x + 7 cos x  13 = 0.
Give your answers to one decimal place.
(Solutions based entirely on graphical or numerical methods are not acceptable.)
(5)

7. 9. Solve, for 360 ≤ x < 540, 12 sin2 x + 7 cos x  13 = 0.
Give your answers to one decimal place.
(Solutions based entirely on graphical or numerical methods are not acceptable.)
(5)
SOLUTION and MARKSCHEME

8. END