Graph sin(theta)=1/2

Problem

sin(θ)=1/2

Solution

1. Identify the goal, which is to find the values of θ that satisfy the equation sin(θ)=1/2 and represent them on a coordinate system.

2. Determine the reference angle by finding the inverse sine of the absolute value of the constant.

(θ_ref)=arcsin(1/2)=π/6

3. Locate the quadrants where the sine function is positive, which are Quadrant I and Quadrant II.

4. Calculate the solutions within the primary interval [0,2*π]

(θ_1)=π/6

(θ_2)=π−π/6=(5*π)/6

5. Generalize the solution to account for the periodicity of the sine function, where n is any integer.

θ=π/6+2*π*n

θ=(5*π)/6+2*π*n

6. Graph the equation by drawing the horizontal line y=1/2 across the graph of the parent function y=sin(θ) The solutions are the θcoordinates of the intersection points.

Final Answer

θ=π/6+2*π*n,(5*π)/6+2*π*n

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