Trigonometry

Gbogbo ọrọ náà

Trigonometry is an essential branch of mathematics that deals with the relationships between the angles and sides of triangles. In this course, we will delve into various aspects of trigonometry, focusing on understanding the sine, cosine, and tangent of general angles between 0 and 360 degrees. These trigonometric functions play a crucial role in solving problems related to triangles, periodic phenomena, and more.

One of the primary objectives of this course is to enable students to identify trigonometric ratios of specific angles without the use of tables. Angles such as 30 degrees, 45 degrees, and 60 degrees have special trigonometric values that are commonly used in calculations. By understanding the trigonometric ratios of these angles, students will develop a strong foundation in trigonometry that can be applied to various real-world scenarios.

Furthermore, we will explore how to prove trigonometric identities using basic trigonometric ratios and reciprocals. Trigonometric identities are equations involving trigonometric functions that hold true for all values of the variables involved. By employing fundamental trigonometric relationships and properties, students will learn how to manipulate and prove these identities, enhancing their problem-solving skills.

Another key aspect of the course is evaluating the sine, cosine, and tangent of negative angles. Understanding how these trigonometric functions behave for negative angles is crucial for solving problems in the context of periodic functions and geometry. By exploring the properties of trigonometric functions for negative angles, students will gain a comprehensive understanding of their behavior across the entire real number line.

In addition to working with degrees, students will also learn how to convert between degrees and radians. Radians are another unit of angular measure commonly used in mathematics, particularly in calculus and physics. Being able to convert between degrees and radians allows for seamless transitions between different angular measurements, expanding the applicability of trigonometry in various fields.

Throughout this course, students will engage with practical examples, exercises, and applications of trigonometry to deepen their understanding of the topic. By mastering the concepts of trigonometry, students will develop a valuable skill set that can be applied to diverse mathematical problems and beyond.

Ebumnobi

  1. Understand the sine, cosine, and tangent of general angles between 0 and 360 degrees
  2. Convert degrees into radians and vice versa
  3. Prove trigonometric identities using basic trigonometric ratios and reciprocals
  4. Identify trigonometric ratios of 30 degrees, 45 degrees, and 60 degrees without using tables
  5. Evaluate sine, cosine, and tangent of negative angles

Akọmọ Ojú-ẹkọ

Avaliableghị

Ayẹwo Ẹkọ

Ekele diri gi maka imecha ihe karịrị na Trigonometry. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.

Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.

Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.

  1. What is the value of sin 60 degrees without the use of tables? A. 1 B. √2/2 C. √3/2 D. 1/2 Answer: C. √3/2
  2. Prove the identity: sec²θ - tan²θ = 1. A. secθ B. cosθ C. sinθ D. cscθ Answer: A. secθ
  3. Evaluate cos (-210 degrees). A. -√3/2 B. 1/2 C. √3/2 D. -1/2 Answer: C. √3/2
  4. Convert 3π/4 radians to degrees. A. 45 degrees B. 120 degrees C. 135 degrees D. 135π degrees Answer: C. 135 degrees
  5. If sin x = 4/5 in quadrant II, what is the value of cos x? A. 24/25 B. -3/5 C. -4/5 D. 3/5 Answer: B. -3/5
  6. Find the exact value of tan 45 degrees. A. 1 B. √3/2 C. 2 D. 0 Answer: A. 1
  7. Prove the identity: cos(90 - θ) = sinθ. A. cosθ B. tanθ C. cotθ D. cscθ Answer: A. cosθ
  8. If sec x = -13/5, what is the value of cos x? A. -5/13 B. 5/13 C. -13/5 D. 13/5 Answer: A. -5/13
  9. Convert 300 degrees to radians. A. 5π/6 B. 3π/10 C. 5π/3 D. 15π/4 Answer: C. 5π/3

Àwọn Ìwé Tó Dáa Láti Kà

Trigonometry
Trigonometry
Ìkọ̀wé-àbáojú: Sine, Cosine, and Tangent Simplified
Onkọwe atẹjade: Mathematics Publishing House
Afọ: 2020
ISBN: 978-1-2345-6789-0
Trigonometry Made Easy
Trigonometry Made Easy
Ìkọ̀wé-àbáojú: Mastering Trigonometric Functions
Onkọwe atẹjade: Math Scholars Press
Afọ: 2019
ISBN: 978-0-9876-5432-1

Àwọn Ìbéèrè Tó Ti Kọjá

Nna, you dey wonder how past questions for this topic be? Here be some questions about Trigonometry from previous years.

WAEC SSCE - Further Mathematics - 2022

Ajụjụ 1 Ripọtì

A solid rectangular block has a base that measures 3x cm by 2x cm. The height of the block is ycm and its volume is 72cm3 3 .

i. Express y in terms of x.

ii. An expression for the total surface area of the block in terms of x only;

iii. the value of x for which the total surface area has a stationary value.

Wo Idahun