Trigonometry (Edexcel IAL Maths P1)

Q: Do I need to memorise the sine rule for Edexcel IAL P1?

Yes. The sine rule, triangle area formula, arc length, and sector area formulae are NOT provided in the P1 formula booklet. Only the cosine rule is printed for you.

Q: Is the ambiguous case of the sine rule tested in P1?

Yes, it is explicitly listed in the 2018 P1 specification, so you should be prepared to identify and solve problems where two possible triangles can be formed from the given measurements.

Q: Do I need to know trigonometric identities like for P1?

No, these identities are part of the P2 syllabus and will not be tested in P1 trigonometry questions.

Edexcel International A-Level Mathematics· 2018 P1 Specification 3.1–3.3· 25 min read

1. 1. Sine Rule, Cosine Rule, and Triangle Area Formula★★★☆☆⏱ 8 min

✓ Calculator OK

This section covers core triangle-solving formulae for P1 trigonometry. You are expected to memorise all formulae except the cosine rule, which is provided in the formula booklet.

📘 Definition

Sine Rule

$\frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C}$ where $a, b, c$ are sides opposite angles $A, B, C$ respectively

Relates side lengths of any triangle to sines of opposite angles, used when you have two angles and one side, or two sides and a non-included angle

Example:

If $a = 5$ cm, $A = 3 0^{\circ}$ , $B = 4 5^{\circ}$ , $b = \frac{5 s i n 4 5 ^{\circ}}{s i n 3 0 ^{\circ}} = 52$ cm

📘 Definition

Cosine Rule

$a^{2} = b^{2} + c^{2} - 2 b c cos A$

Used to find a side when two sides and the included angle are known, or to find an angle when all three sides are known

📘 Definition

Area of a Triangle

$A r e a = \frac{1}{2} ab sin C$

Calculates area of any triangle when you know two sides and the included angle between them

📐 Worked Example

In triangle ABC, AB=7 cm, BC=5 cm, angle BAC=35°. Find the two possible sizes of angle ACB, correct to 1 decimal place.

1
Step 1: Label the triangle: side $a = B C = 5$ cm opposite angle $A = 3 5^{\circ}$ , side $c = A B = 7$ cm opposite angle $C$ (to find)
$\frac{a}{\sin A} = \frac{c}{\sin C}$
2
Step 2: Rearrange to solve for $sin C$
$\sin C = \frac{7 \sin 35^\circ}{5} \approx 0.8030$
3
Step 3: Find the first acute solution
$C = \sin^{-1}(0.8030) \approx 53.4^\circ$
4
Step 4: Find the second obtuse solution using $sin C = sin (18 0^{\circ} - C)$
$C = 180^\circ - 53.4^\circ = 126.6^\circ$
5
Step 5: Verify both angles are valid: $3 5^{\circ} + 53. 4^{\circ} = 88. 4^{\circ} < 18 0^{\circ}$ , $3 5^{\circ} + 126. 6^{\circ} = 161. 6^{\circ} < 18 0^{\circ}$ , so both are correct.

Exam tip:

Always check for the ambiguous case of the sine rule: if the side opposite the given angle is shorter than the other given side, you must give both possible angle values unless the question specifies the triangle is acute/obtuse.

2. 2. Radian Measure, Arc Length and Sector Area★★☆☆☆⏱ 6 min

✓ Calculator OK

Radian measure is an alternative unit for angles that simplifies circular calculations. You must memorise conversion factors and arc/sector formulae, as these are not provided in the P1 formula booklet.

📘 Definition

Radian

One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle. $π$ radians = 180°

Example:

Convert 60° to radians: $60 \times \frac{π}{180} = \frac{π}{3}$ radians. Convert $\frac{π}{2}$ radians to degrees: $\frac{π}{2} \times \frac{180}{π} = 9 0^{\circ}$

📘 Definition

Arc Length

$s = r θ$

Calculates arc length of a circle, where $r$ is radius and $θ$ is central angle in radians

📘 Definition

Sector Area

$A = \frac{1}{2} r^{2} θ$

Calculates area of a sector, where $r$ is radius and $θ$ is central angle in radians

📐 Worked Example

A sector of a circle has radius 8 cm and perimeter 30 cm. Find the area of the sector, giving your answer to 3 significant figures.

1
Step 1: Perimeter of a sector = $2 r + s$ , where $s$ is arc length
$Perimeter = 2(8) + s = 30$
2
Step 2: Solve for arc length $s$
$s = 30 - 16 = 14 \text{ cm}$
3
Step 3: Use $s = r θ$ to find central angle $θ$ in radians
$\theta = \frac{14}{8} = 1.75 \text{ radians}$
4
Step 4: Calculate sector area
$A = 0.5(8^2)(1.75) = 56.0 \text{ cm}^2$

Exam tip:

Always convert angles from degrees to radians before using arc length and sector area formulae. Multiply degrees by $\frac{π}{180}$ to get radians.

3. 3. Graphs of $\text{sin }x$, $\text{cos }x$, $\text{tan }x$: Symmetry and Periodicity★★★☆☆⏱ 7 min

You need to recognise the three core trigonometric graphs, describe their key properties (range, period, symmetry) and identify key points including intercepts, maxima, minima, and asymptotes for $tan x$ .

📘 Definition

Graph of $y = \text{sin }x$

Sinusoidal wave with amplitude 1, period 360° (2π radians). Odd function, symmetric about origin, range $[- 1, 1]$ . Maxima at $9 0^{\circ} + 36 0^{\circ} k$ , minima at $27 0^{\circ} + 36 0^{\circ} k$ for integer $k$ .

📘 Definition

Graph of $y = \text{cos }x$

Sinusoidal wave with amplitude 1, period 360° (2π radians). Even function, symmetric about y-axis, range $[- 1, 1]$ . Maxima at $0^{\circ} + 36 0^{\circ} k$ , minima at $18 0^{\circ} + 36 0^{\circ} k$ for integer $k$ .

📘 Definition

Graph of $y = \text{tan }x$

Periodic function with period 180° (π radians). Vertical asymptotes at $x = 9 0^{\circ} + 18 0^{\circ} k$ for integer $k$ . Range $(- \infty, + \infty)$ .

📐 Worked Example

State the period of the function $y = tan 3 x$ , and give the x-coordinates of the first two positive asymptotes in degrees.

1
Step 1: Recall period of $y = tan (k x) = \frac{18 0 ^{\circ}}{k}$
$Period = \frac{180^\circ}{3} = 60^\circ$
2
Step 2: Asymptotes of $tan 3 x$ occur where $3 x = 9 0^{\circ} + 18 0^{\circ} k$ for integer $k$
3
Step 3: Calculate first two positive asymptotes: for $k = 0$ , $x = 3 0^{\circ}$ ; for $k = 1$ , $x = 9 0^{\circ}$

Exam tip:

Only $tan x$ has a period of 180°; $sin x$ and $cos x$ both have 360° periods. Questions often ask you to match graphs to functions, so memorise these key differences.

4. 4. Exam Strategy for P1 Trigonometry Questions★★☆☆☆⏱ 4 min

📐 Worked Example

A student calculates the area of a triangle with sides 9 cm, 12 cm, included angle 40° as $0.5 * 9 * 12 * sin 40$ , but their calculator is in radian mode. State the error and find the correct area to 3 significant figures.

1
Step 1: Error: The calculator is in radian mode, so it is calculating $sin 40$ radians instead of $sin 40$ degrees.
2
Step 2: Correct calculation in degree mode
$Area = 0.5*9*12*\sin 40^\circ \approx 34.7 \text{ cm}^2$

Exam tip:

Always check your calculator is in the correct mode (degrees or radians) before starting trigonometry questions. Most triangle questions use degrees, while sector/arc questions use radians.

5. Common Pitfalls

Wrong move:

Forgetting to check for the ambiguous case of the sine rule, only giving one angle solution

Why:

When two sides and a non-included angle are given, and the side opposite the given angle is shorter than the other given side, two valid triangles exist, so you lose marks for only giving one answer

Correct move:

Calculate both the acute and obtuse solution for the angle, then check if both sum with the given angle to less than 180° to confirm validity

Wrong move:

Using degree measure in the arc length or sector area formulae

Why:

The formulae $s = r θ$ and $A = \frac{1}{2} r^{2} θ$ only work when $θ$ is in radians, so using degrees gives a massively incorrect answer

Correct move:

Always convert any degree angle to radians first by multiplying by $\frac{π}{180}$ before using these formulae

Wrong move:

Assuming the period of $tan x$ is 360° like $sin x$ and $cos x$

Why:

$tan x$ repeats every 180°, so the period of $tan (k x)$ is $\frac{18 0 ^{\circ}}{k}$ , not $\frac{36 0 ^{\circ}}{k}$ , leading to wrong answers for period and asymptote questions

Correct move:

Memorise that $tan x$ has a unique period of 180° (π radians), separate from $sin x$ and $cos x$

Wrong move:

Trying to use trigonometric identities like $sin^{2} x + cos^{2} x = 1$ in P1 questions

Why:

These identities are part of the P2 syllabus, so P1 questions are designed to be solved without them, wasting time or leading to errors

Correct move:

Use only the sine rule, cosine rule, area formula, radian formulae, and graph properties specified for P1

Wrong move:

Forgetting to show working steps for "show that" questions

Why:

Edexcel awards marks for each valid step of the proof, so even if you get the final answer correct, you lose marks if you skip key steps

Correct move:

Write every step of your working clearly, starting from the given information, to arrive exactly at the stated result

6. Quick Reference Cheatsheet

Concept	Formula/Property	Memorise Required?
Sine Rule	$\frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C}$	Yes
Cosine Rule	$a^{2} = b^{2} + c^{2} - 2 b c cos A$	No (provided in booklet)
Triangle Area	$A r e a = \frac{1}{2} ab sin C$	Yes
Degrees to Radians	$Radians = Degrees \times \frac{π}{180}$	Yes
Arc Length	$s = r θ$ (θ in radians)	Yes
Sector Area	$A = \frac{1}{2} r^{2} θ$ (θ in radians)	Yes
$y = sin x$ period	360° / 2π radians	Yes
$y = cos x$ period	360° / 2π radians	Yes
$y = tan x$ period	180° / π radians	Yes
$tan x$ asymptotes	At odd multiples of 90°	Yes

7. Frequently Asked

Do I need to memorise the sine rule for Edexcel IAL P1?

Yes. The sine rule, $\frac{1}{2} ab sin C$ triangle area formula, arc length, and sector area formulae are NOT provided in the P1 formula booklet. Only the cosine rule is printed for you.

Is the ambiguous case of the sine rule tested in P1?

Yes, it is explicitly listed in the 2018 P1 specification, so you should be prepared to identify and solve problems where two possible triangles can be formed from the given measurements.

Do I need to know trigonometric identities like $sin^{2} x + cos^{2} x = 1$ for P1?

No, these identities are part of the P2 syllabus and will not be tested in P1 trigonometry questions.

Going deeper

official_syllabusEdexcel IAL Maths 2018 SpecificationRefer to section 3.1–3.3 for P1 trigonometry requirements
formula_bookletEdexcel IAL Maths P1 Formula BookletConfirm which formulae are provided for your exam

What's Next

Now that you have mastered core P1 trigonometry, you are ready to practice applying these concepts to structured exam-style questions. Trigonometry is a core, regularly-assessed part of the P1 exam, so consistent practice will help you secure these marks easily. You should also review how trigonometry is combined with other P1 topics like coordinate geometry and differentiation in longer Section B questions, which are common on past papers. Once you are confident with P1 content, you can move on to P2 trigonometry, which covers identities and solving trigonometric equations.