# Trigonometry

## Overview

Trigonometry, a fundamental branch of mathematics, deals with the relationships between the angles and sides of triangles. In this comprehensive course material, we will delve into the intricacies of trigonometry to equip you with the necessary skills to calculate trigonometric ratios, apply special angles in problem-solving, and tackle various real-world scenarios involving angles of elevation and depression, as well as bearings.

One of the primary objectives of this course is to enable you to calculate the sine, cosine, and tangent of angles within the range of -360° ≤ θ ≤ 360°. By understanding these trigonometric ratios, you will gain the ability to analyze and solve geometric problems with precision. Emphasis will be placed on applying special angles such as 30°, 45°, 60°, 75°, 90°, 105°, and 135° to solve trigonometric equations efficiently.

Moreover, we will explore the practical applications of trigonometry in solving problems related to angles of elevation and depression. You will learn how to determine unknown heights or distances using trigonometric functions in scenarios where angles of elevation and depression are involved. These skills are particularly valuable in fields such as engineering, architecture, and surveying.

Another critical aspect of this course is mastering the concept of bearings. Understanding how to interpret and calculate bearings is essential for navigation, cartography, and various spatial applications. You will become proficient in converting angles to bearings and vice versa, enhancing your spatial reasoning and problem-solving abilities.

Furthermore, you will learn how to apply trigonometric formulas to find the areas of triangles accurately. By understanding the relationships between angles and sides in triangles, you will be able to calculate areas efficiently, making geometric computations more manageable and precise.

As you progress through this course material, you will also explore the graphical representation of sine and cosine functions. Understanding the graphs of these trigonometric functions is crucial for visualizing periodic phenomena and analyzing wave-like patterns. You will learn how to interpret and apply sine and cosine graphs to solve various mathematical problems effectively.

By the end of this course, you will have acquired a solid foundation in trigonometry, enabling you to apply your knowledge to a wide range of mathematical, scientific, and practical problems. Whether you are navigating real-world scenarios or delving into advanced mathematical concepts, the skills you gain in this course will be invaluable in your academic and professional pursuits.

## Objectives

1. Solve Problems Involving Sine And Cosine Graphs
2. Apply These Special Angles, Eg 30°, 45°, 60°, 75°, 90°, 105°, 135° To Solve Simple Problems In Trigonometry
3. Solve Problems Involving Bearings
4. Apply Trigonometric Formulae To Find Areas Of Triangles
5. Calculate The Sine, Cosine And Tangent Of Angles Between 360° ≤ Ɵ ≤ 360°
6. Solve Problems Involving Angles Of Elevation And Depression

## Lesson Note

Trigonometry is a branch of mathematics dealing with the relationships between the angles and sides of triangles, particularly right-angled triangles. The foundational principles of trigonometry are pivotal in various fields including physics, engineering, astronomy, and even medicine. This overview aims to provide students with the essential concepts and problem-solving techniques involving trigonometric functions.

## 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. Calculate the cosine of 60 degrees. A. 0 B. 0.5 C. 1 D. √3/2 Answer: √3/2
2. Calculate the value of tan(45 degrees). A. 0 B. 1 C. √2 D. 2 Answer: 1
3. If the length of the opposite side in a right-angled triangle is 5 and the hypotenuse is 13, what is the sine of the angle opposite the opposite side? A. 5/13 B. 13/5 C. 5/12 D. 12/5 Answer: 5/13
4. In a right-angled triangle, what is the value of cos(theta) if the adjacent side is 12 and the hypotenuse is 15? A. 3/4 B. 4/5 C. 15/12 D. 12/15 Answer: 4/5
5. If sin(A) = 0.8 in a right triangle, what is the value of cos(A)? A. 0.8 B. 0.6 C. 0.3 D. 0.4 Answer: 0.6
6. In a right-angled triangle, if the length of the adjacent side is 7 and the hypotenuse is 25, what is the value of tan(theta)? A. 7/24 B. 24/7 C. 7/25 D. 25/7 Answer: 7/24
7. Given that sin(B) = 0.6 in a right triangle, what is the value of tan(B)? A. 0.6 B. 0.8 C. 1.2 D. 1.5 Answer: 0.8
8. If the length of the adjacent side in a right triangle is 3 and the hypotenuse is 5, what is the value of sin(theta)? A. 3/4 B. 4/5 C. 3/5 D. 5/3 Answer: 3/5
9. Calculate the value of cos(30 degrees). A. √3/2 B. 1 C. 0.5 D. 0 Answer: √3/2
10. If the length of the hypotenuse in a right triangle is 10 and the opposite side is 8, what is the value of sin(theta)? A. 0.6 B. 0.8 C. 1.2 D. 1.6 Answer: 0.8

## Past Questions

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

Question 1

In a right angled triangle, if tan  $\theta$ =  $\frac{3}{4}$. What is cos $\theta$ - sin $\theta$?

Question 1

In the diagram above, find x correct to the nearest degree

Question 1

Calculate without using tables Tan 45° + Cos 60°

Practice a number of Trigonometry past questions