Y Snow that cos30 = 4 cos'0-3 cost, Hence or otherwise. a. Find all solutions of the equation:cos 30 in the interval 0s0Sa. %3D b. Solve the equation: 4x-3x= giving your answvers correct to 4 decimal places.
Y Snow that cos30 = 4 cos'0-3 cost, Hence or otherwise. a. Find all solutions of the equation:cos 30 in the interval 0s0Sa. %3D b. Solve the equation: 4x-3x= giving your answvers correct to 4 decimal places.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter7: Analytic Trigonometry
Section7.4: Basic Trigonometric Equations
Problem 2E: The basic equation sinx=2 has_________no/one/infinitely many solutions, whereas the basic equation...
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Solve all Q22 explaining detailly each step
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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