Find all solutions of the equation in the interval [0, 2 pi). Express the soluti

Question

Find all solutions of the equation in the interval [0, 2 pi). Express the solution in radians. Give exact answer 1) cos x = 1/2 2) sin x = squareroot 3/2 3) tan x = squareroot 3 Find all solution of the equation in the interval [0, 2 pi), Round the solution to four decimal places. 4) 5 cos x - 2 = 0 5) 5 tan x + 9 = 0 Find all solution of the equation in the interval [0, 2 pi). Give exact answers when possible 6) sin(x - pi/3) = squareroot 2/2 7) 2 cos(x - pi/8) - squareroot 2 = 0 8) 3 tan(x - pi/4) - squareroot = 0 9) cos 2x = squareroot 2/2 10) (4 cos x - 2)(2 cos x) = 0 11) (tan theta - squareroot 3)(sin theta + 1) = 0 12) tan^2 x = 3 13) 4 sin^2 x - 3 = 0 14) 2 cos^2 theta - 3 cos theta + 1 - 0

Explanation / Answer

Solution:

cos(x) = 1/2

x = /3 +2n and 5/3 + 2n

for [0, 2]

x= /3 and 5/3

(2)

sin(x)= 3/2

x = /3 +2n and 2/3 + 2n

for [0,2]

x = /3 and x =2/3

(3) tan(x ) = 3

x = /3 +n and 4/3 + n

for [0,2]

x = /3 and x =4/3

(4)

5 cos(x) -2 =0

cos(x) = 2/5

x = 2n + cos-1(2/5) and x= 2n - cos-1(2/5)

for [0,2]

x = cos-1(2/5)   and x =2 - cos-1(2/5)

Answer

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