Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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16. i) Find in radians, the general solution of the equation sin + sin30 = sin20. i) Given that f(0)=3 sine +3 cose, express f(0) in the form R sin (0 + a), where R>0 and 0°<a< 90°. 1-x 17.i) show that cos (2 tan" "x) 1+x ii) Find in radians, the general solution of the equation, sin 5x + sin 3x = 0 ii) Express 7 cos 0-5 sin 0 in the form R cos (0+2), where R> 0 and 0<X<90°. giving. R and A correct to one decimal place. Hence, find the value of 0 in the interval 0°<0<360° for which 7 cos0-5 sin 0= 8.6. sine+sin20 18. Show that- = tan 0 1+cos6+ces28 i Find the general solution of the equation sin4x- cos2x 0 19. Find the general solution of the equation cos2x +1 sin2x. ii) Given that f0) = cos0 - V3sin0 express f(0) in the form R cos(0+ a) where R> 0 and 0<as Hence, find the minimum value of 1+f(e) D0. Express 4 sinx -3 cosx in the form R sin(x- a), where a' is an acute angle and R is a positive real number. Find: a All solution of the equation 4sinx- 3cosx 3 in the interval 0° sxS 360", giving your answer to the nearest degree. b. The greatest and least values of 4sinx-3coSN+6 cos A+sin A cos2A+sec2A V21. Venfy that a-b'=(a+b) +(a-bj. Hence show that costA-sin A cos'A+sin'A Find the general solution of the equation: 2. giving your answer in degrees cos A-sin*A Serrect to one decimal place. V Snow that cos30= 4 cos'0-3 cost, Hence or otherwise. a. Find all solutions of the equation:cos 30 in the interval 0s0Sa. b. Solve the equation: 4x-3x= giving your answvers correet to 4 decimal places. 25, i) Show that sin30 = 3 sino - 4 sin30. Hence, or otherwise, solve the equation sin o-sin30 =0, giving all the solutions in the intervai 0° s0<180°. ii) Express g(x), where g(x) = 3 cos 30+ sin30 in the form R cos(30-2) where R>0 and an acute angle. Hence find the general solution of 3eos30 + sin30-2. %3D cos6A+cos2A 24 i Show that Ecot 4A sin6A+sin2A i) Given that f0) = 2 cos0 + sint, express f(0) in the form R cos(0-2), where R>0 and SA Hence obtain the general solution of the equation f(0) !
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Transcribed Image Text:16. i) Find in radians, the general solution of the equation sin + sin30 = sin20. i) Given that f(0)=3 sine +3 cose, express f(0) in the form R sin (0 + a), where R>0 and 0°<a< 90°. 1-x 17.i) show that cos (2 tan" "x) 1+x ii) Find in radians, the general solution of the equation, sin 5x + sin 3x = 0 ii) Express 7 cos 0-5 sin 0 in the form R cos (0+2), where R> 0 and 0<X<90°. giving. R and A correct to one decimal place. Hence, find the value of 0 in the interval 0°<0<360° for which 7 cos0-5 sin 0= 8.6. sine+sin20 18. Show that- = tan 0 1+cos6+ces28 i Find the general solution of the equation sin4x- cos2x 0 19. Find the general solution of the equation cos2x +1 sin2x. ii) Given that f0) = cos0 - V3sin0 express f(0) in the form R cos(0+ a) where R> 0 and 0<as Hence, find the minimum value of 1+f(e) D0. Express 4 sinx -3 cosx in the form R sin(x- a), where a' is an acute angle and R is a positive real number. Find: a All solution of the equation 4sinx- 3cosx 3 in the interval 0° sxS 360", giving your answer to the nearest degree. b. The greatest and least values of 4sinx-3coSN+6 cos A+sin A cos2A+sec2A V21. Venfy that a-b'=(a+b) +(a-bj. Hence show that costA-sin A cos'A+sin'A Find the general solution of the equation: 2. giving your answer in degrees cos A-sin*A Serrect to one decimal place. V Snow that cos30= 4 cos'0-3 cost, Hence or otherwise. a. Find all solutions of the equation:cos 30 in the interval 0s0Sa. b. Solve the equation: 4x-3x= giving your answvers correet to 4 decimal places. 25, i) Show that sin30 = 3 sino - 4 sin30. Hence, or otherwise, solve the equation sin o-sin30 =0, giving all the solutions in the intervai 0° s0<180°. ii) Express g(x), where g(x) = 3 cos 30+ sin30 in the form R cos(30-2) where R>0 and an acute angle. Hence find the general solution of 3eos30 + sin30-2. %3D cos6A+cos2A 24 i Show that Ecot 4A sin6A+sin2A i) Given that f0) = 2 cos0 + sint, express f(0) in the form R cos(0-2), where R>0 and SA Hence obtain the general solution of the equation f(0) !
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