Last updated on Oct 24, 2026

Solving Trig Equations (Leaving Cert Mathematics): Flashcards

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Solving Trig Equations

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3 tools for solving trig equations

Trig identities, inverse functions, symmetry properties

Step 1 of solving trig equations

Isolate the trigonometric function

Step 2 of solving trig equations

Apply inverse functions or known values

Step 3 of solving trig equations

Account for periodicity

Step 4 of solving trig equations

Use identities as needed

Step 5 of solving trig equations

Verify solutions within specified domain

Key Pythagorean trig identity

$sin^2x + cos^2x = 1$

Solutions to $sin x = rac{1}{2}$ in $[0, 2pi]$

$x = rac{pi}{6}, rac{5pi}{6}$

Factorised form of $2cos^2x - cos x - 1 = 0$

$(2cos x + 1)(cos x - 1) = 0$

Solutions to $cos x = - rac{1}{2}$ in $[0, 2pi]$

$x = rac{2pi}{3}, rac{4pi}{3}$

Solution to $cos x = 1$ in $[0, 2pi]$

$x = 0$

3 common tools for solving trig equations

Inverse functions, unit circle, trig identities

Applications of trig equations

Geometry, physics, engineering contexts

What the unit circle helps find in trig equations

Angles where trig functions have specific values

Explore Leaving Cert Mathematics Revision Notes by Topics

The Basics

Special Angles & The Unit Circle

Radians & Sectors

Periodic Functions