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By Sarah Thompson BSc (Hons) Mathematics, PGCE
Trig is one of the most important topics in maths, as it links together the angles and sides in triangles and provides a platform for advances into the areas of physics, engineering and A Level Maths. Many students find trig difficult at first, but once it is understood and tackled in the right way, it follows logically from the first principles and can even be fun. In this article we look at ten expert tips to help you master this topic and improve your examination results.
Firstly, understand the three basic trigonometrical ratios, namely the sine, cosine and tangent. These ratios link the relationships between sides and angles in right-angled triangles. To help remember them, use the simple formula SOH CAH TOA. Regular practice on a wide range of problems will encourage confidence in applying them in any question encountered.
Next turn your attention to the unit circle. This is one of the most useful devices in solving trigonometrical problems since it will enable you to find the sine, cosine and tangent values of any angle. The unit circle can be drawn and labelled so that a firm grasp of how these functions behave can be obtained without merely knowing the trig value of triangles.
Thirdly, learn the key angle values, namely 0°, 30°, 45°, 60° and 90°. They are used very frequently in A Level and GCSE exam questions. Knowing the values of their sines, cosines and tangents will save valuable time in the examination. The fourth tip is employ the CAST rule. This tells you which trigonometric function is positive in which quadrant. It is an excellent method of avoiding sign errors in equations or angles of more than 90°.
Fifth, learn your trigonometric identities, like sin²θ + cos²θ = 1 thoroughly. These identities help you in the simplification of equations and learning to tackle higher problems.
The sixth tip is be diligent in solving trigonometric equations. Make sure you can find all possible solutions in a given range, as it is often a specified requirement in A Level examinations.
Seventh, study the graphs of sin, cos and tan, their behaviour, their periods and shape. This gives an insight into the correct interpretation of graph questions.
Eighth, work confidently in radians as well as degrees. The use of radians is frequent in higher maths, thus ensure that you satisfactorily switch from one to the other as of need.
Ninth check your numerical settings, ensure it is in the right mode, either radians or degrees before starting a question.
Finally, consistency is necessary. All round solid revision, plus guided study makes a remarkable difference. Attend an A Level Maths Revision Course in October — an excellent idea for getting geared up with its expert support, and practice will help you feel confident for your exams.
Trigonometry does not have to be difficult. With these ten trustful tips and through steady practice a solid grasp of important mathematical principles and understanding will be built up strong enough for you to be ready for whatever lies ahead.
Author Bio:
Sarah Thompson, BSc. (Hons) Mathematics, PGCE Sarah is a qualified A Level Maths tutor and a former sixth-form teacher, having spent some twelve years in the classroom teaching. She acts as a specialist in all things dealt with in connection with trigonometry, calculus, and examination preparation. Her approach to the teaching is one of clarity, confidence, and practical interpretation of problems. She has literally helped hundreds of students attain excellent and worthy A Level grades, through use of discrete lessons, with focused revision strategies.
