Trigonometry + trigonometric equations

Dr Kevin Olding

In this course you'll start by looking in depth at the sine and cosine rules for the area of a triangle. You'll think carefully about how to extent the definitions of sin cos and tan to angles of any size and to solve. You'll learn about some exact forms for these ratios and be confident in solving equations using sin cos and tan. This will including quadratics in these functions and problems where you have to apply trigonometric identities before solving the equation.

Worksheets with full video solutions will guide you through problems of a range of difficulties, including routine examples to get the hang of the basics as well as some very tough challenge style problems that will stretch you to fully master the ideas.

What You Will Learn

Sine and Cosine Rules and Areas of Triangles: Be confident using the cosine and sine rules (including the ambiguous case), finding the area of any triangle and applying these to a range of problems.
Equations and Identities Involving sin(x), cos(x) and tan(x): Master solving trigonometric equations, including using the range of values to determine the correct solutions, as well as using identities so solve quadratics in sin and cos and a range of other equations.
Solve challenging problems: After solving a mixture of introductory GCSE and A-level style problems and harder maths challenge style problems, all with video solutions, you'll have really mastered the topics.

Who This Course is For

This course is for anyone who is interested to learn about trigonometry and trigonometric equations, but may be particularly suited to:

  • Advanced GCSE or IGCSE students looking to master the hardest topics
  • Students in the summer before starting, or in the first year of A-Level maths
  • Typical students for this course are aged 14-17 but it may also be useful for younger students or adult learners

Curriculum

59 Lessons
Welcome to the course!
Sine rule 1
Sine rule 2 - the ambiguous case
Cosine rule
Area of a triangle
Bearings
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Worksheet D1: Sine and cosine rules and area of a triangle
Question 1 abc
Question 1 def
Question 2
Question 3
Question 4
Question 5
Question 6 hint
Question 6
Bouns: Proof of sine and cosine rules (Mathsaurus YouTube)
Solving equations involving sin(x) for any angle
Solving equations involving cos(x) for any angle
Solving equations involving tan(x) for any angle
Worksheet D2: Solving trig equations for any angles
Question 1
Question 2
Question 3
Question 4 hint
Question 4
Question 5 hint
Question 5
Exact values of sin cos and tan
Exact values beyond 90 degrees
Worksheet D3 - Exact trigonometric ratios
Question 1
Question 2
Question 3
Question 4 hint
Question 4
Question 5
Harder trig equations part 1
Harder trig equations part 2
Worksheet D4 - Solving harder trig equations
Question 1
Question 2
Question 3 hint
Question 3
Question 4 hint
Question 4
Question 5 hint
Question 5
tanx=sinx/cosx
sin^2(x)+cos^2(x)=1
Example using tanx=sinx/cosx
Example using sin^2(x)+cos^2(x)=1
Worksheet D5 - Using trig identities to solve equations
Question 1
Question 2
Question 3 hint
Question 3
Question 4 hint
Question 4

Teacher

instructor

Dr Kevin Olding

Kevin Olding is the creator of Mathsaurus. He has a First Class MMATH Mathematics degree from Magdalen College, Oxford and a PhD from the University of Bath, as well as an MSc in Applied Statistics from Birkbeck, University of London (Distinction and prize for best overall performance), an MRes in Statistical Applied Mathematics from the University of Bath, and a degree in Law. Before creating Mathsaurus, Kevin taught maths in London at Westminster School and Dulwich College and also at Birkbeck College (University of London).

  • 4.5 hours of video content
  • 59 Lessons
  • Trigonometry + Trigonometric Equations
This course also includes:
  • Video tutorials
  • 5 pdf worksheets
  • Video solutions for all problems
  • Self-paced and available 24/7
£29 - 1 year access Or free for members - sign up here

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