2. i) Find in radians the values of x in the interval 0°< x <360° which satisfy the dquation cos2x - sin2x = 1. ii) Find in radians the general solution of the equation cos5x + cos3x=0 iii) Express cosx-v3 sin x in the form R cos(x +2) where R>0 and 2 is and acute angle. Hence find the maximum and minimum values of: -cosx-V3 sinx.
2. i) Find in radians the values of x in the interval 0°< x <360° which satisfy the dquation cos2x - sin2x = 1. ii) Find in radians the general solution of the equation cos5x + cos3x=0 iii) Express cosx-v3 sin x in the form R cos(x +2) where R>0 and 2 is and acute angle. Hence find the maximum and minimum values of: -cosx-V3 sinx.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
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.
Question
Solve all Q2 explaining detailly each step
Transcribed Image Text:cose
cose
1. (YShow that for sin0 +1,
2 sec0
1+sing
1-sino
(ii) For 0°s 0 180°, find to the nearest tenth of a degree the solution of the equition
cos o = cos°0.
(ii)Express 3eos0 +6 sine= V22.5, giving the general solution in degrees.
2. i) Find in radians the values of x in the interval 0°<x<360° which satisfy the equatioa
cos2x- sin2x = 1.
ii) Find in radians the general solution of the equation cos5x + cos3x 0
ii) Express cosx-v3 sin x in the form R cos(x + ) where R>0 and 2 is and acute angle.
Hence find the maximum and minimum values of: -cosx-V3 sinx.
3. Express 1+cos2x in terms of cos x. hence
a. Evaluate (1 + cosx)dx
b. Express 1-cos2x in terms of t, where t=
4. a. Find to the nearest degree the value of 0 in the range 0°s0 s 360° for which
sin'o + 2cos20=2 cos0.
b. Express 4cos0 + 3sin0 in the form R cos(0 - a), R>0 and a is an acute angle, giving the
value of a to the nearest tenth of a degree. Hence, find, to the nearest dearee, the range of
values of 0 between 0o and 360° for which 4 cos0 +3sin0<3.
5. ) Find the value of 0 for which cos20- 2cos0 = 3, in the interval: 0°<0<27.
ii) Find in radians the ge solution of the equation sin20 - V3 cos0 0.
ii) Given that f(0) = 12 sin 0-5 cos0, express f(0) in the formr sin (0 - a) where r>0 and
tan
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38
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