Quiz

General Solution

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General Solution

Quiz

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Quiz

Find the general solution to the following equations:

cot (2x - 60^o) = -3^1/2

4 cos 2y + 3 sin 2y = 0

sin z + sin 3z + sin 5z = 0

Scroll below for the answers.

Solution:

cot (2x - 60^o) = -3^1/2

tan (2x - 60^o) = -3^-1/2

2x - 60^o = 180^on + 150^o

x = 90^on + 105^o

Solution:

4 cos 2y + 3 sin 2y = 0

5 cos (2y - 36.870^o) = 0 R-formula

cos (2y - 36.870^o) = 0

2y - 36.870^o = 360^on + 90^o or 360^on - 90^o

y = 180^on + 63.4^o or y = 180^on -26.6^o

Solution:

sin z + sin 3z + sin 5z = 0

sin 3z cos 2z + sin 3z = 0

sin 3z (cos 2z - 1) = 0

sin 3z = 0 or cos 2z = 1

3z = np 2z = 2np

z = np/3 ...(1) z = np ...(2)

Since (2) is a subset of (1), the final solution is

z = np/3