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Trigonometric equations for SQA Higher Maths

Trigonometric equations

This page covers the following topics:

1. Simple trigonometric equations
2. Moderate trigonometric equations
3. Complex trigonometric equations
4. Solving trigonometric equations graphically

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

Solve cosยฒ(x + 4ยบ) โˆ’ 1 = 0 for 0ยฐ < x < 360ยฐ.

x = 176ยบ, 356ยบ

Solve cosยฒ(x + 4ยบ) โˆ’ 1 = 0 for 0ยฐ < x < 360ยฐ.

2

Solve sin(x + 70ยบ) = 0.5 for 0ยฐ < x < 360ยฐ.

x = 80ยฐ, 320ยบ

Solve sin(x + 70ยบ) = 0.5 for 0ยฐ < x < 360ยฐ.

3

Solve sinx = 0.5 graphically over the range 0 < x < 2ฯ€.

image

Solve sinx = 0.5 graphically over the range 0 < x < 2ฯ€.

4

Solve tan40ยฐ = 2sinx + 1 for 0ยบ < x < 360ยบ.

x = 185ยฐ, 355ยฐ

Solve tan40ยฐ = 2sinx + 1 for 0ยบ < x < 360ยบ.

5

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

image

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

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