Further Pure Mathematics - 4PM1 PearsonEdexcel

Trigonometric Ratios And Graphs

Muhtasari

Trigonometric ratios connect angles to lengths, and their graphs reveal the repeating patterns that underpin everything from sound waves to satellite orbits. Mastering the exact values for the standard angles and knowing how sine, cosine and tangent behave beyond the first quadrant is the gateway to every other trigonometry topic in the 4PM1 specification.

In this lesson you will learn to evaluate sin, cos and tan for any angle, sketch the three core graphs from memory, recall the exact values for 30, 45 and 60 degrees (and their radian equivalents), and use symmetry to find trigonometric ratios of related angles in all four quadrants.

Malengo

Know the three basic trigonometric ratios of angles of any magnitude in degrees or radians
Sketch and use the graphs of sine, cosine and tangent
Know the exact values for sine, cosine and tangent of 30, 45 and 60 degrees and their radian equivalents
Use exact values to find the trigonometric ratios of related angles

Ramani ya mawazo

Mada hii imechorwa ili uone jinsi mawazo yanavyounganika.

Fungua ramani ya mawazo kwenye programu

Kadi za kumbukumbu

Mazoezi ya haraka ya kumbukumbu kuhusu kinachopimwa katika mada hii.

Fanya mazoezi ya kadi hizi kwenye programu

Maelezo ya Somo

Every triangle you have ever solved relied on the relationship between an angle and the ratio of two sides. In Further Pure Mathematics those ratios extend far beyond right-angled triangles: sine, cosine and tangent are defined for every real number, and their graphs repeat in elegant, predictable cycles that model oscillations across science and engineering.

Dokezo Kamili la Somo Linapatikana kwenye Programu ya Green Bridge

Pata programu ya Green Bridge CBT kwenye simu au kompyuta yako kwa maktaba kamili ya IGCSE: mitihani ya miaka iliyopita, miongozo ya usahihishaji, ramani za mawazo, kadi za marudio na masomo ya sauti.

Maelezo kamili ya masomo yenye michoro

Msaidizi wa kujifunza wa AI

Mitihani ya majaribio yenye muda, husahihishwa mara umalizapo

Pakua programu ya simu Pakua programu ya kompyuta

Inapatikana kwa Android, Windows, macOS, na Linux Programu ya iOS inakuja hivi karibuni

Tathmini ya Somo

Hongera kwa kukamilisha somo la Trigonometric Ratios And 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.

What is the exact value of sin 30 degrees? A) 1 B) 1/2 C) sqrt(3)/2 D) 1/sqrt(2) Answer: B
In which quadrant is the angle 300 degrees? A) First B) Second C) Third D) Fourth Answer: D
What is the period of the tangent function? A) 90 degrees B) 180 degrees C) 270 degrees D) 360 degrees Answer: B
What is the exact value of cos 135 degrees? A) 1/sqrt(2) B) -1/sqrt(2) C) sqrt(3)/2 D) -sqrt(3)/2 Answer: B
The graph of y = sin(theta) crosses the theta-axis at which of these points? A) 0, 90, 180 B) 0, 180, 360 C) 90, 270 D) 0, 90, 270 Answer: B

Fanyia kazi maswali haya kwenye programu

Vitabu Vinavyopendekezwa

Pearson Edexcel International GCSE (9-1) Further Pure Mathematics Student Book

Manukuu: First edition

Mchapishaji: Pearson Education

Mwaka: 2017

ISBN: 978-0-435-18831-7

Maelezo: Endorsed student book covering the full 4PM1 specification.

Jifunze zaidi kutoka vyanzo huria

Sehemu ya kitabu Unit Circle OpenStax · Algebra and Trigonometry
Find function values for the sine and cosine of 30° or ( π 6 ) , 45° or ( π 4 ) , 30° or ( π 6 ) , 45° or ( π 4 ) , and 60 ∘ or ( π 3 ) . 60 ∘ or ( π 3 ) .

"Algebra and Trigonometry: Unit Circle" 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/7-3-unit-circle. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
Sehemu ya kitabu The Other Trigonometric Functions OpenStax · Algebra and Trigonometry
Find exact values of the trigonometric functions secant, cosecant, tangent, and cotangent of π 3 , π 4 , π 3 , π 4 , and π 6 . π 6 .

"Algebra and Trigonometry: 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/7-4-the-other-trigonometric-functions. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction

Vimechapishwa na mashirika mengine chini ya leseni huria na vinatajwa kama wanavyoomba. Viungo hufungua tovuti zao.

Fanya Mazoezi ya Maswali ya Majaribio

Ungependa kufanya mazoezi ya maswali ya majaribio kuhusu Trigonometric Ratios And Graphs? Pakua programu ya Green Bridge CBT ili kupata maswali ya majaribio na tathmini kamili za mazoezi kuhusu mada hii.

Pakua Programu Kwenye Google Playstore

Kila kitu unachohitaji ili kufaulu katika JAMB, WAEC & NECO.

Msaidizi wa Gumzo wa Kujifunza wa AI Uliobinafsishwa

Maswali ya mtihani zaidi ya 200,000 ya IGCSE, JAMB, WAEC na NECO

Zaidi ya Madaftari ya Masomo 1200

Msaada Nje ya Mtandao - Jifunze Wakati Wowote, Popote Pale

Ratiba ya Daraja la Kijani

Muhtasari wa Fasihi na Maswali Yanayoweza Kutokea

Fuata Utendaji na Maendeleo Yako

Maelezo ya Kina kwa Kujifunza kwa Kina