00_(3)_2016_-_2017_H2_Maths_Trigonometry_Practice_Questions_(student)

National Junior College Mathematics Department 2016 Revision: Trigonometry Page 1 of 5 National Junior College 2016 – 2017 H2 Mathematics Revision: Trigonometry Practice Questions Basic Mastery Questions Basic Trigonometric Functions 1. By using a right-angled triangle, show that (a) sin cos ,2    (b) cos sin ,2    (c) tan cot .2    Remark: Even though we have only justified the above results for an acute angle  , in fact these relationships hold for all values of . 2. It is given that 120 .A Without using a calculator, w rite down the smallest positive integer n such that each of the following trigonometric expression yields a positive value. Justify your answer clearly. (a) sin( ),nA (b) tan( ),nA (c) cos( ).nA Relationship between Basic Trigonometric Functions and their inverses 3. Find the exact value of   1cos tan 1 . 4. It is given that 1tan , x  where x is positive. (a) State the range of possible values of . (b) Find the following in terms of x: (i) cot , (ii) sec , (iii) cosec . Use of Formulae 5. It is given that 11tan and tan .23AB Evaluate    tan and tan 2A B A without the use of a calculator. 6. Express sin 3 cosxx in the form sin ( )Rx  , where 0R and 0 2  are constants whose exact values are to be determined. Trigonometric Equations 7. Write down the basic angle for 1cos . 2x Hence solve 1cos , 2x where 0 2 .x  8. Write down the basic angle for 1tan . 3 x Hence solve 1tan , 3 x where 0 2 .x  9. Solve sin 2 0, where 0 2 .4xx      

National Junior College Mathematics Department 2016 Revision: Trigonometry Page 2 of 5 Sine and Cosine Rule 10. The diagrams above (not drawn to scale) show four triangles. Find the possible value(s) of (a) ,ABC (b) ,DF (c) HI, (d) .JLK Intermediate Level Questions Compound Angle Formulae 1. Given that 3sin 5A and 12cos , 13B prove that one possible value of cos( )AB is 33 ,65 and find all the other possible values. [J80/P1/4] Proving Trigonometric Identities 2. Prove the following identities: (a) sin 1 cosec ,1 cos 2 2 A AA (b) 2 2cos 2cos , 2 xx (c) 44cos sin cos 2 ,   (d) cos sin tan ,cos sin 4 xx xxx     (e) sin 5 sin cot 2 ,cos5 cos     (f) 1 sin 6sin 3 cos 3 .4 4 2 xxx              Trigonometric Equations 3. Solve sin 2 sin , where 0 2 .x x x    (Attempt this question using two approaches: Factor and Double angle formula). 4. Solve 2sin 2 sin 2 2, where 0 2 .x x x     Sine and Cosine Rule 5. The diagram (not drawn to scale) show triangle XYZ. Find the lengths of XY and YZ. 6. A triangle has side lengths 6 cm, 8 cm and 11 cm. Find the smallest angle in the triangle.

National Junior College Mathematics Department 2016 Revision: Tri