# StudySquare

# Trigonometric equations for SQA Higher Maths

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.

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

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

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

# 1

Solve cos²(x + 4º) − 1 = 0 for 0° < x < 360°.

x = 176º, 356º

# 2

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

x = 80°, 320º

# 3

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

image

# 4

Solve tan40° = 2sinx + 1 for 0º < x < 360º.

x = 185°, 355°

# 5

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

image

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