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Edexcel A-level Maths Trigonometric equations

Trigonometric equations

This page covers the following topics:

We can solve trigonometric equations using the reference angles and trigonometric identities that have been learnt, as well as basic algebra.

Simple trigonometric equations

We can solve trigonometric equations using the reference angles and trigonometric identities that have been learnt, as well as basic algebra.

Moderate trigonometric equations

We can solve trigonometric equations using the reference angles and trigonometric identities that have been learnt, as well as basic algebra.

Complex trigonometric equations

We can use the sine, cosine and tangent graphs to solve trigonometric equations graphically.

Solving trigonometric equations graphically

1

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Solve sin(x + 70ΒΊ) = 0.5 for 0Β° < x < 360Β°.

Edexcel A-level Maths Trigonometric equations Solve sin(x + 70ΒΊ) = 0.5 for 0Β° < x < 360Β°.
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2

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Solve sinΒ²(60ΒΊ) = 1 + x.

Edexcel A-level Maths Trigonometric equations Solve sinΒ²(60ΒΊ) = 1 + x.
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3

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Find x from 3 + 4cos2x = 1 for βˆ’180Β° < x < 180Β°.

Edexcel A-level Maths Trigonometric equations Find x from 3 + 4cos2x = 1 for βˆ’180Β° < x < 180Β°.
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4

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Solve for 0Β° < x < 360Β°, 2sinΒ²x + 5sinx βˆ’ 3 = 0.

Edexcel A-level Maths Trigonometric equations Solve for 0Β° < x < 360Β°, 2sinΒ²x + 5sinx βˆ’ 3 = 0.
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5

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Solve, for 0 < x < 2Ο€, sinΒ²(x) βˆ’ sin(x) = 2.

Edexcel A-level Maths Trigonometric equations Solve, for 0 < x < 2Ο€, sinΒ²(x) βˆ’ sin(x) = 2.
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6

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Solve, for 0Β° ≀ x ≀ 180Β°, tan(2x) = 5sin(2x).

Edexcel A-level Maths Trigonometric equations Solve, for 0Β° ≀ x ≀ 180Β°, tan(2x) = 5sin(2x).
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7

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Solve for βˆ’180Β° < x < 180Β°, (18tanx)(5sinx βˆ’ 2) = 0.

Edexcel A-level Maths Trigonometric equations Solve for βˆ’180Β° < x < 180Β°, (18tanx)(5sinx βˆ’ 2) = 0.
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8

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Solve cosΒ²(x) + cos(x) = sinΒ²(x) for 0ΒΊ < x < 360ΒΊ.

Edexcel A-level Maths Trigonometric equations Solve cosΒ²(x) + cos(x) = sinΒ²(x) for 0ΒΊ < x < 360ΒΊ.
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9

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By sketching a graph, we can find that for cos2x = βˆ’cosx, in the interval 0ΒΊ < x < 270ΒΊ, x = 60Β°, 180Β°. Sketch this graph showing the intersection points of the curves.

Edexcel A-level Maths Trigonometric equations By sketching a graph, we can find that for cos2x = βˆ’cosx, in the interval 0ΒΊ < x < 270ΒΊ, x = 60Β°, 180Β°. Sketch this graph showing the intersection points of the curves.
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10

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By sketching a graph, solve 4sinx = 2sinx + 2 for 0ΒΊ < x < 360ΒΊ.

Edexcel A-level Maths Trigonometric equations By sketching a graph, solve 4sinx = 2sinx + 2 for 0ΒΊ < x < 360ΒΊ.
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