# Trigonometry

## Overview

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.

## Objectives

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

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## Lesson Evaluation

Congratulations on completing the lesson on Trigonometry. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.

You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.

Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.

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

## Past Questions

Wondering what past questions for this topic looks like? Here are a number of questions about Trigonometry from previous years

Question 1

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.

Practice a number of Trigonometry past questions