Mathematics - Additional - 0606 CIE

Amplitude, Period And Trigonometric Graphs

Muhtasari

Stretching and shifting the basic sine, cosine and tangent graphs produces a whole family of curves. Two numbers control most of it: the amplitude (how tall the wave is) and the period (how often it repeats).

In this lesson you will understand and use the amplitude and period of a trigonometric function, and draw and use the graphs of \(y = a \sin bx + c\), \(y = a \cos bx + c\) and \(y = a \tan bx + c\).

Malengo

Understand and use the amplitude and period of a trigonometric function, including the relationship between graphs of related trigonometric functions.
Draw and use the graphs of y = a sin bx + c, y = a cos bx + c and y = a tan bx + c.

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Maelezo ya Somo

Amplitude and period describe any oscillation, from sound waves to tides, and let you sketch transformed trig graphs quickly.

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Hongera kwa kukamilisha somo la Amplitude, Period And Trigonometric Graphs. Sasa kwa kuwa umechunguza dhana na mawazo muhimu, ni wakati wa kuweka ujuzi wako kwa mtihani. Sehemu hii inatoa mazoezi mbalimbali maswali yaliyoundwa ili kuimarisha uelewaji wako na kukusaidia kupima ufahamu wako wa nyenzo.

Utakutana na mchanganyiko wa aina mbalimbali za maswali, ikiwemo maswali ya kuchagua jibu sahihi, maswali ya majibu mafupi, na maswali ya insha. Kila swali limebuniwa kwa umakini ili kupima vipengele tofauti vya maarifa yako na ujuzi wa kufikiri kwa makini.

Tumia sehemu hii ya tathmini kama fursa ya kuimarisha uelewa wako wa mada na kubaini maeneo yoyote ambapo unaweza kuhitaji kusoma zaidi. Usikatishwe tamaa na changamoto zozote utakazokutana nazo; badala yake, zitazame kama fursa za kukua na kuboresha.

For y = 3 sin 2x, the amplitude is: A. 2 B. 3 C. 6 D. 180 Answer: B
For y = 3 sin 2x, the period is: A. 90° B. 180° C. 360° D. 720° Answer: B
In y = a sin bx + c, the period is: A. a B. 360/b C. b/360 D. c Answer: B
In y = a sin bx + c, the constant c: A. changes amplitude B. changes period C. shifts the graph vertically D. has no effect Answer: C
The amplitude of y = 5 cos x is: A. 1 B. 5 C. 10 D. 360 Answer: B

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Vitabu Vinavyopendekezwa

Cambridge IGCSE Mathematics Core and Extended Coursebook

Manukuu: Second edition

Mchapishaji: Cambridge University Press

Mwaka: 2018

ISBN: 978-1-108-43718-9

Maelezo: Endorsed coursebook with full coverage of the 0580/0980 syllabus, worked examples and practice exercises.

Cambridge IGCSE Core and Extended Mathematics

Manukuu: Fifth edition

Mchapishaji: Hodder Education

Mwaka: 2023

ISBN: 978-1-398-37391-4

Maelezo: Endorsed textbook with worked examples and graded questions across Core and Extended content.

Jifunze zaidi kutoka vyanzo huria

Sehemu ya kitabu Graphs of the Sine and Cosine Functions OpenStax · Algebra and Trigonometry
Graph variations of y = sin ( x ) y = sin ( x ) and y = cos ( x ) y = cos ( x ) .

"Algebra and Trigonometry: Graphs of the Sine and Cosine Functions" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/8-1-graphs-of-the-sine-and-cosine-functions. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
Sehemu ya kitabu Graphs of the Other Trigonometric Functions OpenStax · Algebra and Trigonometry
Analyze the graph of y=tan x.

"Algebra and Trigonometry: Graphs of the Other Trigonometric Functions" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/8-2-graphs-of-the-other-trigonometric-functions. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction

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