Manual PreCalculus: Trigonometric Functions (Quick Review Notes)

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The answer of these were provided in great detail.

Inverse Trig Functions - Quick Review Graph the function...

This course provides a solid grounding for any student who is about to start learning calculus. I thoroughly recommend it. But omg, after a while it just clicked and I could understand it. Especailly compared to other courses online, I would definitely say this is prob the hardest, maybe not the MOST thorough, but its proofs are rigorous as math should be, and is definitely a taste of what REAL math is, if you know what I mean.

Thank you for the great time!!


  1. Course summary?
  2. Calculus with Julia.
  3. The Maverick Strain: A Call to Arms (The Richard Finch Series Book 4);
  4. 5. Trigonometric Functions and Graphs;
  5. Graphs of Trig Functions.
  6. Early Explorations In Science (Exploring Primary Science and Technology).
  7. Trigonometry/Pre-Calculus.

Francis's teaching was excellent, clear easy to understand and rigorous. I found the other course tutors unclear and difficult to understand at times and although their working was correct they did seem to overcomplicate explanations and often used a slightly different notation to Francis, so I did find this a bit confusing. I am disappointed that the course has come to an end. I do hope that there will be more courses like this in future as I have really enjoyed it.. A very thorough course well presented with worked solutions to help if in difficulty.

Any comments posing questions are answered very quickly by course staff, I think they must work shifts to give such immediate responses, the most attentive monitoring of all the courses that I have done.

By Susan Cooper-Nguyen

I am just sorry that owing to other commitments I fell behind on this particular course, very rare for me not to complete a course. I shall probably sign up when it is re-run. I appreciate a highly professional instruction, plenty of problems of varied difficulty to solve accompanied by a detailed solution of the problems both in videos and in pdf files, interesting applications of presented mathematical concepts, lots of quizes that prepare students for the tests, the support of the educators in answering students' questions. Taking part in the course was a great adventure. This is a very enjoyable, yet very serious course covering lots of different areas of Mathematics.

My suggestion is that it will be better if Francis uses focus-directrix definition of conic section when deriving the canonical equation of ellipse, parabola, and hyperbola since it is much easier to understand. Other than that, I can safely say that this is the most impressive PreCalculus course that I have ever taken in my life.

A well designed course that is challenging, interesting and informative.

MATH Precalculus

The educators explained the material well and guided learners through problems. They were ready to take part in the forum with further explanation and responded promptly to correct occasional inaccuracies. It has been a very well prepared and presented course. We covered a wide range of topics including functions, trigonometry and geometry just to mentioned a few. At the end of each topic there was a set of questions to be answered. I would strongly recommend it.


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  • It was hard work and challenging. I didn't understand everything but by the end I felt I had learnt a great deal. It did pretty much what I hoped it would do and left me hoping that there will be another course by the same team soon. This course was very interesting although I feel like it had some parts that where very hard and some that where very easy Maybe my understanding of some parts where bad and some good.

    The course was perfect for me.

    Pre-Calculus FINAL REVIEW 108 questions Answered

    The professors explained the material very well. I think that with so many topics the course should take a bit longer and there should be more exercises. Very clearly presented with a good standard format. Challenging but careful working through was repaid. Recommended for any novice mathematician who is keen to learn more. Very interesting and fun! The theorem and how it applies to special right triangles are set out here:. In pre-calculus you deal with inequalities and you use interval notation to express the solution set to an inequality. The following formulas show how to format solution sets in interval notation.

    Never fear, the following formulas show you how to deal with absolute values in pre-calculus. Of course you use trigonometry, commonly called trig, in pre-calculus. And you use trig identities as constants throughout an equation to help you solve problems. The always-true, never-changing trig identities are grouped by subject in the following lists:.

    Three things demonstrated to me the high quality of the course development: - The student is obliged to make their own notes, just copying the course text and downloading the videos and pdfs is insufficient when faced with quiz and test questions. This ensures that the topic is learnt. It also provides a check for the student that they have understood sufficient of the previous content.

    These are only provided once the question has been answered. One of the best Future Learn courses that I have done. I have signed up for over 40 courses so far, and this easily rates amounts the best. The course content was comprehensive. It set its target at the correct audience. The material is challenging but provides a correct in depth discussion of the subject. The material was presented in informative, friendly lectures which were easy to understand. This was backed up with extensive challenging exercises.

    The answer of these were provided in great detail. This course provides a solid grounding for any student who is about to start learning calculus. I thoroughly recommend it. But omg, after a while it just clicked and I could understand it. Especailly compared to other courses online, I would definitely say this is prob the hardest, maybe not the MOST thorough, but its proofs are rigorous as math should be, and is definitely a taste of what REAL math is, if you know what I mean.

    Thank you for the great time!! Francis's teaching was excellent, clear easy to understand and rigorous. I found the other course tutors unclear and difficult to understand at times and although their working was correct they did seem to overcomplicate explanations and often used a slightly different notation to Francis, so I did find this a bit confusing.

    I am disappointed that the course has come to an end. I do hope that there will be more courses like this in future as I have really enjoyed it.. A very thorough course well presented with worked solutions to help if in difficulty.

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    Advanced Precalculus: Geometry, Trigonometry and Exponentials

    Any comments posing questions are answered very quickly by course staff, I think they must work shifts to give such immediate responses, the most attentive monitoring of all the courses that I have done. I am just sorry that owing to other commitments I fell behind on this particular course, very rare for me not to complete a course.

    I shall probably sign up when it is re-run. I appreciate a highly professional instruction, plenty of problems of varied difficulty to solve accompanied by a detailed solution of the problems both in videos and in pdf files, interesting applications of presented mathematical concepts, lots of quizes that prepare students for the tests, the support of the educators in answering students' questions.

    Trigonometric Functions and the Unit Circle

    Taking part in the course was a great adventure. This is a very enjoyable, yet very serious course covering lots of different areas of Mathematics. My suggestion is that it will be better if Francis uses focus-directrix definition of conic section when deriving the canonical equation of ellipse, parabola, and hyperbola since it is much easier to understand. Other than that, I can safely say that this is the most impressive PreCalculus course that I have ever taken in my life.

    A well designed course that is challenging, interesting and informative. The educators explained the material well and guided learners through problems. They were ready to take part in the forum with further explanation and responded promptly to correct occasional inaccuracies. It has been a very well prepared and presented course. We covered a wide range of topics including functions, trigonometry and geometry just to mentioned a few. At the end of each topic there was a set of questions to be answered.

    I would strongly recommend it.