Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 40E
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Question
Solve all Q27 explaining detailly each step
Transcribed Image Text:Study aid in Advanced level Mathemaries...
R>0 and tan for 0< <Hence or otherwise, find the minimum value of
1 ig(0)
ii)Use the expansion of (sin'e + cos 0) to show that sin'o + cos*0 = (3 + cos"0). Hence or
otherwise find in radians, the general solution of the equation sin'o + cos"0 = 4. (MTA)
26. i) Express: 5cos0- 12sin0 in the form: Reos(0 + a) giving the values of R>0 and a to the
nearest degree. Hence find the maximum and minimum values of
3.
15cose-12sinel+2
sin30+sine
2tane
27. i) Show that
cos30+cose
1-tan2e
fi Prove that: sin(sin 0 - cos 0) = 20 –1 for 0s0S (MTA)
28. Find the general solution of the equation cos2x + 1 = cosx(2008)Q5(1)
sina+sinß
29 i) Prove that
cot()
cosa-cosB
ii) find in radians, the general solution of the equation: tan2x tanx = -1
30. (i) Find the general solution of the equation Cose + 2 sin 0 =0
(i) Express f(x), where f(x) = cosx + sinx, in the form R cos(x -2), where R>0 and ). is an
(2009)Q3
acute angle. Hence, find the value of x for which the minimum value of
occurs.
(2010)Q7
31. show that cos2A =
1-tan A
1+tan A
37Find, in radians, the general solution of the equation cos2x +!= sin2x. (2011)Q3
i) Find the general solution of the equation: sin 26 = sine.
i) f(x) = cos x+2sin x.
a) Fxpress f(x) in the form: rcos(x-x), wherer> 0 and 0<oc < 90°.
b) Find to the nearest tenth of a degree, the set of values of x which satisfy the equation:
cos x+ 2sin x = 1.
c) Show that: -V5 s cos x + 2 sin xs V5.(2012)07
3 i) Given that: f(x)= v3 cos x + sin x, express f(x) in the form: Rcos (x - A). Where R>
Oand 0 <1<. Hence find the general solution of the equation: f(x) = v3
sin 2x+sin 4x
ii) Prove that:
= tan 2x. Hence find the general solution of the equation:
1+cos 2x+cos 4x
1+cos 2x+cos 4x
-- 0.
(2013)Q3
sin 2x+sin 1x
34 Express cosx + V3 sin x in the form R cos (x - A), where R> 0 and 0 < A<
Hence find
(a) The general solution of the equation cosx + vV3 sin x = V3
(b) The maximum and mininmum values of cos x + V3 sin x + 2(2014)02
sin 0+sin 20
$5. (i) show that:
= tan 0
1+cos 0+cos 20
(ii)Find the general solution of the equation sin 4x + cos 2x = 0
nSolve for x ,where0" < xa the equation sin 3x + cos x = 0(2015)02
41
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