sin0- wina t genera m to ge \"[]\"kis any integer Simplifty your answer. Use ang

Question

sin0- wina t genera m to ge "[]"kis any integer Simplifty your answer. Use angle measures greater than or equal to 0 and less than 2x. Type an exact answer, using xa k as the variable) an exact answer, using x as needed. Use integers or fractions for any numbers in the expression. Type an expression using all the solutions to sin2 based on the larger angle k is any integer k as the variable.) List the first six solutions that are greater than or equal to (Simplity your answer. Type an exact answer, using x as needed. Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed) MacBook A Air 4 0 2

Explanation / Answer

sintheta = -sqrt3/2

theta = sin^-1(sqrt(3)/2 +pi ( smaller angle)

theta = pi/3 +pi = 4pi/3

general solution:

theta = 4pi/3 + 2k*pi

Larger angle

theta = 2pi - sin^-1(sqrt(3)/2)

= 2pi - pi/3 = 5pi/3

general solution:

theta = 5pi/3 + 2k*pi

First six solution:

theta = 4pi/3 , 5pi/3 , 4pi/3 +2pi , 5pi/3 +2pi, 4pi/3 +4pi, 4pi/3 +6pi

= 4pi/3 , 5pi/3 , 10pi/3 , 11pi/3 , 16pi/3 , 22pi/3

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