A-Level Maths OCR B (MEI) H640

Know how to solve right-angled triangles using trigonometry.

Be able to use the definitions of $\sin{θ}$, $\cos{θ}$ and $\tan{θ}$ for any angle.

By reference to the unit circle, $\sin{θ}=y$, $\cos{θ}=x$, $\tan{θ}=\dfrac{y}{x}$.

Know and use the graphs of $\sin{θ}$, $\cos{θ}$ and $\tan{θ}$ for all values of $θ$, their symmetries and periodicities.

Stretches, translations and reflections of these graphs.

Combinations of these transformations.

Notation:

• Period

Know and be able to use the exact values of $\sin{θ}$ and $\cos{θ}$ for $θ = 0°, 30°, 45°, 60°, 90°$ and the exact values of $\tan{θ}$ for $θ = 0°, 30°, 45°, 60°$.

Know and be able to use the fact that the area of a triangle is given by $\dfrac{1}{2}ab\sin{C}$.

Know and be able to use the sine and cosine rules.

Use of bearings may be required.

Understand and be able to use $\tan{θ} = \dfrac{\sin{θ}}{\cos{θ}}$

e.g. solve $\sin{θ} = 3\cos{θ}$ for $0° \le θ \le 360°$.

Understand and be able to use the identity $\sin^2{θ} + \cos^2{θ} = 1$.

e.g. solve $\sin^2{θ} = \cos{θ}$ for $0° \le θ \le 360°$.

Be able to solve simple trigonometric equations in given intervals and know the principal values from the inverse trigonometric functions.

e.g. $\sin{θ} = 0.5$, in $[0°, 360°] \iff θ = 30° ,150°$

Includes equations involving multiples of the unknown angle e.g. $\sin{2θ} = 3\cos{2θ}$.

Includes quadratic equations.

Notation:

• $\arcsin{x} = \sin^{-1}{x}$
• $\arccos{x} = \cos^{-1}{x}$
• $\arctan{x} = \tan^{-1}{x}$

Excludes: General solutions.

Know and be able to use exact values of $\sin{θ}$, $\cos{θ}$ and $\tan{θ}$ for $θ = 0, \dfrac{\pi}{6}, \dfrac{\pi}{4}, \dfrac{\pi}{3}$, $\pi$ and multiples thereof and $\sin{θ}$, $\cos{θ}$ for $θ = \dfrac{\pi}{2}$ and multiples thereof.

Understand and use the definitions of the functions $\arcsin$, $\arccos$ and $\arctan$, their relationship to $\sin$, $\cos$ and $\tan$, their graphs and their ranges and domains.

Understand and use the definition of a radian and be able to convert between radians and degrees.

Know and be able to find the arc length and area of a sector of a circle, when the angle is given in radians.

The results $s = rθ$ and $A = \dfrac{1}{2}r^2θ$ where $θ$ is measured in radians.

Understand and use the standard small angle approximations of sine, cosine and tangent.

$\sin{θ} = θ$, $\cos{1-\dfrac{θ^2}{2}}$, $\tan{θ}$ where $θ$ is in radians.

Understand and use the definitions of the $\sec$, $\cosec$ and $\cot$ functions.

Including knowledge of the angles for which they are undefined.

Understand relationships between the graphs of the $\sin$, $\cos$, $\tan$, $\cosec$, $\sec$ and $\cot$ functions.

Including domains and ranges.

Understand and use the relationships $\tan^2{θ} + 1 = \sec^2{θ}$ and $\cot^2{θ} + 1 = \cosec^2{θ}$.

Understand and use the identities for $\sin{(θ \pm ϕ)}$, $\cos{(θ \pm ϕ)}$, $\tan{(θ \pm ϕ)}$.

*Includes understanding geometric proofs. The starting point for the proof will be given.

Excludes: Proofs using de Moivre’s theorem will not be accepted.*

Know and use identities for $\sin{2θ}$, $\cos{2θ}$, $\tan{2θ}$.

Includes understanding derivations from $\sin{(θ \pm ϕ)}$, $\cos{(θ \pm ϕ)}$, $\tan{(θ \pm ϕ)}$.

• $\cos{2θ} ≡ \cos^2{θ} - \sin^2{θ}$
• $\cos{2θ} ≡ 2\cos^2{θ} - 1$
• $\cos{2θ} ≡ 1 - 2\sin^2{θ}$

Understand and use expressions for $a \cos{θ} \pm b \sin{θ}$ in the equivalent forms $R\sin{(θ \pm α)}$ and $R\cos{(θ \pm α)}$.

Includes sketching the graph of the function, finding its maximum and minimum values and solving equations.

Use trigonometric identities, relationships and definitions in solving equations.

Construct proofs involving trigonometric functions and identities.

Use trigonometric functions to solve problems in context, including problems involving vectors, kinematics and forces.

The argument of the trigonometric functions is not restricted to angles.