TMUA Trigonometry

TMUA tests trigonometry A LOT! Everything is up for testing, from knowing common trigonometric values (such as sin 150) to being able to sketch trigonometric graphs, solve trigonometric equations, use common trigonometric identities (sin^2 + cos^2 = 1 etc) and sum various unusual series involving trigonometry (such as sin^2 (1) + sin^2 (2) + ...).   

For those so interested, we offer both one to one TMUA coaching on trigonometry, as well as online group coaching via Zoom - 'TMUA Trigonometry' is Session #7 of 20' . Check our TMUA Group Coaching Schedule page for dates when these sessions are available - details of what we cover in each group session can be found on our TMUA Coaching Sessions Overview page. For more general information on our online sessions check out our  'Online Coaching FAQ'.

Feel free to contact us if you require more information regarding any of the above.

Free Revision Resources

The below list of questions links to short videos (teasers) on our YouTube channel which directly or indirectly test elements of what is required to succeed in answering TMUA questions on trigonometry - they also provide a detailed solution to the question posed, together with tips and tricks and are arranged roughly in increasing order of difficulty. All the videos are taken from the Gresty Academy YouTube podcast 'A Crash Course in TMUA Must Know Maths' which contains hundreds of TMUA style questions and is great for revision.

• Teaser #214 - tests understanding of the graph y=A cos (Bx-C) - Fairly Mild
• Teaser #436 - tests ability to find smallest value of x satisfying cos (ax+b) = y - Standard
• Teaser #147 - tests how to find tan 2x given tan(x/2) - Standard
• Teaser #32 - tests understanding of complement and supplement of an angle to calculate tan (x) - Standard
• Teaser #250 - tests knowledge of how to convert cosec x to tan x taking account of signs - Standard
• Teaser #309 - tests double angle formulae and finding sec and tan given cosec - Standard
• Teaser #281 - tests how to evaluate both trig values and manipulate surds mentally - Standard
• Teaser #287 - tests knowledge of sin and cos double angles - Standard
• Teaser #193 - tests application of double angle formulae twice - Standard
• Teaser #456 - tests how to find the minimum value of abs(x) given a trig equation - Medium
• Teaser #452 - tests finding sec(x), cosec(x) and cot(x) given tan(x/2) - Medium
• Teaser #449 - tests how to find A when sin^2(Ax) satisfies f(x)=f(x+2) - Medium
• Teaser #435 - tests ability to use formula for tan(2x) to find tan(pi/12) - Medium
• Teaser #490 - tests ability to find a maximum of an exponential trigonometric expression - Medium
• Teaser #486 - tests recognition of a well known functional inequality involving trig options - Medium
• Teaser #424 - tests ability to find fraction of an interval where sin(3x)>=1/2 - Medium
• Teaser #132 - tests ability to solve equation involving tan (x/2) - Medium
• Teaser #416 - tests knowledge of t-formulae to solve a trig equation - Medium
• Teaser #275 - tests whether composites of even and odd functions (including powers of sin and cos) are even, odd or neither - Medium
• Teaser #501 - tests understanding of a well known functional inequality - Medium
• Teaser #153 - tests how to solve an equation involving cos(sin(x)) - Medium
• Teaser #484 - tests ability to use symmetry and patterns to sum a tricky looking trigonometric series - Medium
• Teaser #113 - tests ability to solve an equation involving sin and cos for a specific range - Medium
• Teaser #79 - tests ability to arrange graphs according to their gradient at a point - Medium
• Teaser #297 - tests ability to notice that a quadratic in x is actually a tan double angle formula - Medium
• Teaser #419 - tests understanding of an inequality and how it affects possible values of cos theta - Medium
• Teaser #204 - tests ability to solve an equation involving multiple 'tan' taking advantage of graphical symmetry - Medium
• Teaser #427 - tests ability to arrange various expressions in increasing order by clever approximations - Medium
• Teaser #273 - tests ability to notice that a quadratic in x is actually a cos double angle formula - Medium
• Teaser #496 - tests criteria for which a triangle is described uniquely - Medium
• Teaser #171 - tests ability to solve an equation involving multiple 'sin' taking advantage of graphical symmetry - Medium
• Teaser #500 - tests understanding of when sqrt(x^2) = (sqrt(x))^2 - Medium
• Teaser #308 - tests manipulation of trig identities and then finding the minimum value using extreme values of sin(2x) - Medium
• Teaser #394 - tests ability to solve an equation involving cos (2x) and sin (2x) - Medium
• Teaser #420 - tests ability to find number of solutions to x^2 sin(2x)=cos(2x) - Quite Tough
• Teaser #468 - tests ability to find all solutions of cos(A)=cos(B) - Quite Tough
• Teaser #464 - tests how to solve a horrific looking trig inequality by reducing it to a much simpler one - Quite Tough
• Teaser #503 - tests understanding of how to find when an integral approximation of y=sin^2(x) underestimates the area - Quite Tough
• Teaser #444 - tests ability to solve two trig inequalities and find the fraction of a range satisfying both - Quite Tough
• Teaser #482 - tests ability to find the second smallest positive solution to a trig equation - Quite Tough
• Teaser #461 - tests ability to establish which functional equations (some involving trig) have solutions and which don't - Quite Tough
• Teaser #492 - tests ability to use graphical methods and a symmetry trick to solve a tough looking modulus equation - Quite Tough
• Weekend Workout #4 - tests ability to find sin^2(x) given tan(x)  - Quite Tough
• Teaser #284 - tests knowledge that arithmetic mean >= geometric mean to find a minimum of a complex trig expression - Quite Tough
• Teaser #480 - tests ability to split a function into its odd and even components to solve a functional equation - Quite Tough
• Teaser #262 - tests noticing even and odd functionality to massively simplify an integral - Quite Tough

TMUA Past Questions on Trigonometry: SP p1 q2; SP p1 q10; SP p1 q18; SP p2 q11; 2016 p1 q8; 2016 p1 q10; 2016 p1 q17; 2016 p2 q3; 2016 p2 q17; 2017 p1 q8; 2017 p2 q4; 2017 p2 q8; 2017 p2 q12; 2018 p1 q6; 2018 p1 q18; 2018 p1 q19; 2018 p1 q20; 2018 p2 q4; 2018 p2 q13; 2019 p1 q13; 2019 p1 q14; 2019 p1 q17; 2019 p1 q19; 2019 p2 q6; 2020 p1 q12; 2020 p1 q18; 2020 p2 q2; 2020 p2 q9; 2020 p2 q15; 2021 p1 q6; 2021 p1 q14; 2021 p1 q17; 2021 p1 q19; 2021 p2 q5; 2021 p2 q18; 2021 p2 q19; 2022 p1 q1; 2022 p1 q9; 2022 p1 q14; ; 2022 p1 q16; 2022 p2 q18; 2022 p2 q20; 2023 p1 q4; 2023 p1 q9; 2023 p1 q12; 2023 p1 q15; 2023 p2 q5; 2023 p2 q12

Practice makes perfect - good luck in your studies!