Solve the equation. Give a general formula for all the solutions. List all the s

Question

Solve the equation. Give a general formula for all the solutions. List all the solutions k = 0, 1, and 2. cos theta = -1/2 Write the general form for all the solutions to cos theta = -1/2 based on the smaller angle. theta = (Simplify your answer. Type an exact answer, using pi as needed. Use integers or fractions for any numbers in Write the general form for all the solutions to cos theta = -1/2 based on the larger angle. theta = (Simplify your answer. Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the List the solutions for k = 0, 1, and 2. theta = (Simplify your answer. Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the

Explanation / Answer

cos theta = - 1/2

theta = cos ^-1 ( -1/2)

= 2pi/3 + 2 pi* k , 4pi/3 + 2pi*k

smaller angle is 2pi/3 + 2 pi* k

larger angle is 4pi/3 + 2pi*k

solutions for k = 0

2pi/3 , 4 pi/3

k = 1

2pi/3 + 2pi = 8pi/3   

4pi/3 + 2pi = 10pi/3

k =2

2pi/3 + 4pi = 14pi/3

4pi/3 + 4pi = 16pi/3

solutions are :

theta = 2pi/3 , 4pi/3 , 8pi/3 , 10pi/3 , 14pi/3 , 16pi/3

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