Last updated on Oct 23, 2026

Effect of Adding a Constant to Sin/Cos Function (Leaving Cert Mathematics): Flashcards

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Effect of Adding a Constant to Sin/Cos Function

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Transformation from adding constant to $\sin(x)$ or $\cos(x)$

Vertical shift

General form of vertical shift for sine function

$y = \sin(x) + k$

Property changed by adding constant to $\sin(x)$ or $\cos(x)$

Midline

Effect when $k > 0$ in $y = \sin(x) + k$

Graph shifts upward by $k$ units

Effect when $k < 0$ in $y = \cos(x) + k$

Graph shifts downward by $|k|$ units

New midline after vertical shift by $k$

$y = k$

Effect on amplitude when constant added to $\sin(x)$

Remains the same

Period of $\sin(x) + k$ or $\cos(x) + k$

$2\pi$

Effect on frequency when constant added to $\cos(x)$

Remains the same

Role of new midline $y = k$ for the wave

Centre of oscillation

Explore Leaving Cert Mathematics Revision Notes by Topics

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Special Angles & The Unit Circle

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Explore Leaving Cert Mathematics Model Answers by Topics

The Basics

Special Angles & The Unit Circle

Radians & Sectors

Periodic Functions

Solving Trig Equations

Trig Identities

Explore Leaving Cert Mathematics Quizzes by Topics

The Basics

Special Angles & The Unit Circle

Radians & Sectors

Periodic Functions

Solving Trig Equations

Trig Identities

Explore Leaving Cert Mathematics Exam Questions by Topics

The Basics

Special Angles & The Unit Circle

Radians & Sectors

Periodic Functions

Solving Trig Equations

Trig Identities

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