Let o,= 2 (cos 45° + i sin 45°), @,= (cos 30° + i sin 30°), calculate a. @j @2= b. o, / 0,= с. О d. 0,1/5) = (Hint: there are 5 roots for ,"5) )

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 1E: Because the trigonometry functions are periodic, if a basic trigonometric equation has one solution,...
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Please solve Q.4

3. Given
sin 0° = 0,
sin 30° = 1/2,
sin 45° = v(2) /2, cos 45° = v(2) /2,
cos 0° = 1,
%3D
cos 30° = v(3) /2,
veird Superf0ods You Must Try! - Hey, a lew days ago, you came to our websSite and took
sin 60°
sin 90° = 1,
V(3) /2, cos 60° = 1/2,
cos 90° = 0,
Express the following complex numbers in the form a + bi,
a. 5(cos 0° + i sin 0°)
b. 2(cos 30° + i sin 30°)
c. V(2) (cos 45° + i sin 45°)
d. V(3) (cos 60° + i sin 60°)
e. 3(cos 90° + i sin 90°)
4. Let w,= 2 (cos 45° +i sin 45°), @,= (cos 30° + i sin 30°), calculate
a. W, W2=
b. 0, / @2°
3
с. О
d. 02"
%3D
(1/5)
(Hint: there are 5 roots for o,5))
(1/5)
Transcribed Image Text:3. Given sin 0° = 0, sin 30° = 1/2, sin 45° = v(2) /2, cos 45° = v(2) /2, cos 0° = 1, %3D cos 30° = v(3) /2, veird Superf0ods You Must Try! - Hey, a lew days ago, you came to our websSite and took sin 60° sin 90° = 1, V(3) /2, cos 60° = 1/2, cos 90° = 0, Express the following complex numbers in the form a + bi, a. 5(cos 0° + i sin 0°) b. 2(cos 30° + i sin 30°) c. V(2) (cos 45° + i sin 45°) d. V(3) (cos 60° + i sin 60°) e. 3(cos 90° + i sin 90°) 4. Let w,= 2 (cos 45° +i sin 45°), @,= (cos 30° + i sin 30°), calculate a. W, W2= b. 0, / @2° 3 с. О d. 02" %3D (1/5) (Hint: there are 5 roots for o,5)) (1/5)
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