Solve the equation for exact solutions over the interval $[0^{\circ}, 360^{\circ})$ .
$6 \sin (\frac{θ}{2}) = 6 \cos (\frac{θ}{2})$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is ${$ \}
(Type an integer or a decimal. Type your answer in degrees. Do not include the degree symbol in your answer. Use a comma fo separate answers as needed.)
B. The solution is the empty set.

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Final Answer: The solution set is $90$ .

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Step 1 ：The given equation is $6 \sin (\frac{θ}{2}) = 6 \cos (\frac{θ}{2})$ . We can simplify this equation by dividing both sides by 6, which gives us $\sin (\frac{θ}{2}) = \cos (\frac{θ}{2})$ .

Step 2 ：We know that $\sin (\frac{θ}{2}) = \cos (\frac{θ}{2})$ when $\frac{θ}{2} = 45^{\circ}$ or $\frac{θ}{2} = 225^{\circ}$ , because $\sin 45^{\circ} = \cos 45^{\circ}$ and $\sin 225^{\circ} = \cos 225^{\circ}$ .

Step 3 ：So, we can solve for $θ$ by multiplying both sides of the equation by 2. This gives us $θ = 90^{\circ}$ and $θ = 450^{\circ}$ . However, since we are looking for solutions in the interval $[0^{\circ}, 360^{\circ})$ , we discard the solution $θ = 450^{\circ}$ .

Step 4 ：Therefore, the solution to the equation is $θ = 90^{\circ}$ .

Step 5 ：Final Answer: The solution set is $90$ .

Answer

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