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

Question

Solve the equation. Give a general formula for all the solutions. List six solutions Write the general form for all the solutions to cos based on the smaller angle. e-k is any integer (Simplify your answer. Use angle measures greater than or equal to 0 and less than 2x. Type an exact answer, using x as needed. Use integers or fractions for any numbers in the expression. Type an expression using k as the variable.) Write the general form for all the solutions to cos 2 based on the larger angle. 0-?, k is any integer (Simplify your answer. Use angle measures greater than or equal to 0 and less than 2, Type an exact answer, using ? as needed. Use integers or fractions for any numbers in the expression. Type an expression using k as the variable) List the first six solutions that are greater than or equal to 0. (Simplify 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.)

Explanation / Answer

cos theta /2 = 1/2

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

theta /2 = pi/3 + 2 kpi

theta /2 = 5pi/3 + 2kpi

theta = 2pi/3 + 4kpi ( based on smaller angle )

theta = 10pi/3 + 4kpi ( based on larger angle )

six solutions are

theta = 2pi/3 , 10pi/3 , 14pi/3 , 22pi/3 , 26pi/3 , 34pi/3

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