(a) (i) Use de Moivre's theorem to express cos 40 and sin 40 in terms of cos 0 and sin 0. 4 tan3 0 4 tan 0 – (ii) Hence prove that tan 40 1 - 6 tan² 0 + tan4 0` (iii) Deduce that tan' -1 24 -1 1 4 tan 7 3'
(a) (i) Use de Moivre's theorem to express cos 40 and sin 40 in terms of cos 0 and sin 0. 4 tan3 0 4 tan 0 – (ii) Hence prove that tan 40 1 - 6 tan² 0 + tan4 0` (iii) Deduce that tan' -1 24 -1 1 4 tan 7 3'
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter1: The Six Trigonometric Functions
Section1.5: More On Identities
Problem 97PS
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![12. (a) (i) Use de Moivre's theorem to express cos 40 and sin 40 in terms of cos 0 and sin 0.
4 tan 0 – 4 tan3 0
1 – 6 tan? 0 + tan 0
(ii) Hence prove that tan 40
-1 24
(iii) Deduce that tan
-1 1
4 tan 3.
7
(b) Hence find the four fourth roots of 7 + 24i in Cartesian form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd5b7bbe-0385-445f-a431-8477178458c3%2F752379d5-8154-4fc2-94e4-c5ffa0dc5316%2F5or85lb_processed.png&w=3840&q=75)
Transcribed Image Text:12. (a) (i) Use de Moivre's theorem to express cos 40 and sin 40 in terms of cos 0 and sin 0.
4 tan 0 – 4 tan3 0
1 – 6 tan? 0 + tan 0
(ii) Hence prove that tan 40
-1 24
(iii) Deduce that tan
-1 1
4 tan 3.
7
(b) Hence find the four fourth roots of 7 + 24i in Cartesian form.
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