Free Course Image Trigonometry Grade 11

Free online courseTrigonometry Grade 11

Duration of the online course: 4 hours and 29 minutes

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Enhance your understanding of trigonometry with this comprehensive Grade 11 course. Covering key topics like triangle CAST, reductions, identities, and general solutions.

In this free course, learn about

  • Right Triangles and CAST Diagram Basics
  • Angle Reduction and CAST Applications
  • Angle Reduction Practice and Exam Preparation
  • Algebraic Identities and Simplification with Reduction
  • Core Trigonometric Identities Practice
  • Advanced Identity Manipulation
  • Solving Basic Trigonometric Equations
  • Relating Angles and Reference Angles
  • Equations Involving tan and sin² Transformations
  • Mixed Reduction and Identity Applications
  • Exam-Style Questions: Identities and Graph Context
  • Angle Determination and Special Values
  • Final Practice: Simplification and Equation Solving

Course Description

Welcome to "Trigonometry Grade 11," an essential course designed for students venturing into the fascinating world of trigonometric concepts and applications. With a total duration of 4 hours and 29 minutes, this comprehensive course provides an in-depth exploration of the key topics and fundamental principles central to Grade 11 Trigonometry. While there are no reviews yet, this course stands out as an impeccable resource in the realm of Basic Studies, particularly within the specific subcategory of Trigonometry.

The journey begins with an introduction to the Triangle on CAST, guiding learners through the vital trigonometric concepts and providing practical exercises to solidify understanding. This foundation is critical for comprehending more intricate topics. Following this, students will encounter Reduction Techniques, which delve into using numbers and special angles effectively in various trigonometric contexts. A series of practice sessions ensure that these reduction skills are well-practiced and thoroughly understood.

Mastery in trigonometry requires rigorous practice, and this course does not fall short; it includes an array of practical exercises and exams, ensuring concepts are ingrained and skills are honed. To reinforce learning, several practice sessions are interspersed throughout, leading to practical applications and assessments. These provide ample opportunity to encounter real exam questions and scenarios, thereby preparing students comprehensively for any challenges they face in their examinations.

Identities form another pivotal aspect of this course, with a structured introduction and extensive practice sessions focusing on understanding and applying trigonometric identities. These sections systematically build up the necessary skills to manipulate and simplify trigonometric expressions, a crucial competency for all advanced mathematical studies.

As the course progresses, students will also focus on the General and Specific Solutions of trigonometric equations, segmented into digestible parts for enhanced comprehension. Various practice modules accompany these sections, providing hands-on experience in solving a range of trigonometric problems, ensuring solid proficiency in navigating through different solution strategies.

With multiple assessment opportunities strategically placed throughout the course, students are consistently tested on their knowledge and understanding, receiving immediate feedback to aid their learning process. These regular evaluations not only facilitate self-assessment but also encourage a deeper grasp of the material covered.

By the end of this course, students will not only be well-versed in the core topics of Grade 11 Trigonometry but also highly proficient in applying these concepts in various practical and exam settings. Enroll in "Trigonometry Grade 11" to embark on an educational journey that thoroughly prepares you for academic success in trigonometry!

Course content

  • Video class: Trigonometry grade 11: Triangle on CAST 23m
  • Exercise: Given that \( \sin(\theta) = \frac{3}{5} \), \( \theta \) is in the second quadrant, and you need to find \( \cos(\theta) \). What is \( \cos(\theta) \)?
  • Video class: Trigonometry grade 11: Triangle on CAST Practice 02m
  • Exercise: Given a right triangle where one of the angles is 37 degrees and the sine of this angle is k, which of the following expressions represents cos(53 degrees) in terms of k?
  • Video class: Trigonometry grade 11: Triangle on CAST Practice 02m
  • Exercise: Given a right triangle in which one vertex lies at the origin and another at (-5, -12), what is the value of sin α, where α is the angle opposite the vertical leg of the triangle?
  • Video class: Reduction grade 11 21m
  • Exercise: Using the CAST diagram, which of the following is the correct reduction for sin(270 - x)?
  • Video class: Reduction grade 11: Using Numbers and special angles. 16m
  • Exercise: Given the trigonometric expression tan(720 - x), which quadrant does the angle correspond to on the CAST diagram and how can it be simplified?
  • Video class: Reduction grade 11: practice 17m
  • Exercise: If \( \sin(90^\circ - x) \) equals \( \cos(x) \), which trigonometric identity does this statement represent based on complementary angles?
  • Video class: Reduction Grade 11: Exam 04m
  • Exercise: Evaluate the following expression using trigonometric identities: cos(178°) + cos(179°) + cos(180°).
  • Video class: Reduction grade 11: practice 03m
  • Exercise: Simplify the expression sin(360 - x) - 1 to a single trigonometric term.
  • Video class: Reduction grade 11: practice 01m
  • Exercise: If sin(θ + 180°) = -sin(θ), what trigonometric identity can be used to simplify this expression?
  • Video class: Reduction grade 11: practice 03m
  • Exercise: Which trigonometric identity equation is equivalent to the expression: (-cos²x + 1) / (sin²x)?
  • Video class: Reduction grade 11: practice 04m
  • Exercise: What is the simplified value of the expression cos(130°) + sin(400°) if you consider the properties of trigonometric functions and their respective quadrants?
  • Video class: Identities Grade 11: Introduction and practice 25m
  • Exercise: What is the value of sin^2(θ) + cos^2(θ) for any angle θ?
  • Video class: Identities Grade 11: Practice 03m
  • Exercise: In a trigonometric expression, you are tasked with simplifying tan²(x) - sin²(x) to one of the standard trigonometric identities. If you let tan(x) be represented as sin(x)/cos(x), what does the expression simplify to?
  • Video class: Identities Grade 11: Practice 03m
  • Exercise: Which of the following trigonometric identities is correct?
  • Video class: Identities Grade 11: Practice 03m
  • Exercise: Which of the following trigonometric expressions is equivalent to cot(x)?
  • Video class: Identities Grade 11: Practice 02m
  • Exercise: When you simplify the expression (sin x / (1 + cos x)) + (1 / tan x), what will it become?
  • Video class: Identities Grade 11: Practice 01m
  • Exercise: Which of the following expressions simplifies to 1 using trigonometric identities?
  • Video class: General and Specific Solution grade 11:Part 1 15m
  • Exercise: Solve the trigonometric equation \( \tan(x) = -\sqrt{3} \) for \( x \) in the interval \( [0, 360) \) degrees.
  • Video class: General and Specific Solution grade 11: Part 2 17m
  • Exercise: In solving the equation 2tan(x) = tan(x) + 3, what is the value of x in degrees for 0 ≤ x < 360?
  • Video class: General Solution Grade 11: Practice 07m
  • Exercise: In a typical cosine graph, the function is undefined for certain values of d. Which of the following intervals represent the range of values where the function is defined?
  • Video class: General Solution Grade 11: Practice 04m
  • Exercise: What is the value of sin(x) if you solve the equation 3sin²(x) + 5sin(x) - 2 = 0 using the quadratic formula?
  • Video class: General Solution Grade 11: Practice 06m
  • Exercise: If sin(x) = cos(30° - x), what is the value of angle x?
  • Video class: General Solution Grade 11: Practice 02m
  • Exercise: Given the equation: sin(a - 30) = sin(a), where a is in the interval [0, 360] degrees, find the general solution and specify the values of a within the given interval.
  • Video class: General Solution Grade 11: Practice 02m
  • Exercise: What is the reference angle for the trigonometric expression when you perform an inverse sine operation on 0.4?
  • Video class: General Solution Grade 11: Practice 02m
  • Exercise: Given that 3tan(x) = 2, what is the reference angle for x?
  • Video class: General Solution Grade 11: Practice 04m
  • Exercise: Given the equation sin(x) - 2(1 - sin²(x)) + 2 = 0, what are the solutions for x in terms of k, where k is an integer?
  • Video class: Identities grade 11 02m
  • Exercise: In trigonometry, when simplifying the expression \( \frac{2 \, \sin x}{1 - \sin^2 x} \), which identity can be directly applied to simplify the denominator?
  • Video class: Reduction grade 11: practice 03m
  • Exercise: Simplify the following trigonometric expression as much as possible: sin(40°) × sin(x) / (cos(50°) × tan(x)).
  • Video class: Identities grade 11 03m
  • Exercise: Given that sin²(x) + cos²(x) = 1, which of the following identities is correct?
  • Video class: Trigonometry Grade 11 Exam Question 08m
  • Exercise: If a point T is located on the line segment OP where O is the origin and OP is 25 units long, and the coordinates of P are (-7, 24), what are the coordinates of T if OT is 15 units long?
  • Video class: Trigonometry Grade 11 Exam Question 07m
  • Exercise: Simplify the trigonometric expression (sin^2(x) / (4 * cos(90° + x))) into a single trigonometric term.
  • Video class: Trigonometry Grade 11 Exam Question 07m
  • Exercise: Consider a triangle on the Cartesian plane where point P is at (-7, 4). Using this triangle, what is the value of cos(θ) for θ being the angle at point P with reference to the horizontal? Assume the hypotenuse is calculated using Pythagoras' theorem.
  • Video class: General Solution Grade 11: Exam 06m
  • Exercise: Determine the general solution for the equation cos(2x) = 0.
  • Video class: Trigonometry Grade 11 Exam Question 04m
  • Exercise: In a triangle, angle α is such that tan(α) = -3/4. If angle α is in the second quadrant, what is the measure of angle α?
  • Video class: Reduction grade 11: Exam 04m
  • Exercise: Given a trigonometric expression: -sin(30) * tan(30), what is the simplified result without using a calculator?
  • Video class: Identities grade 11 01m
  • Exercise: What is the equivalent expression of \( \frac{\sin(x) (1 - \cos(x))}{\cos(x)} \)?
  • Video class: Grade 11 Trigonometry Exam Questions 04m
  • Exercise: Simplify the following expression to a single trigonometric ratio, without using a calculator: (1 - sin² θ) / cos θ.
  • Video class: General Solution Grade 11 Exam Questions 05m
  • Exercise: Solve the equation 3 tan(4X) = -2 cos(4X) for X and determine which solutions are valid.
  • Video class: Trigonometry Grade 11 Exam Questions 04m
  • Exercise: What is the minimum value of the function f(x) = 1 - sin(x)?

This free course includes:

4 hours and 29 minutes of online video course

Digital certificate of course completion (Free)

Exercises to train your knowledge

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