Verify the Identity sin(theta)=1/2

Problem

sin(θ)=1/2

Solution

1. Identify the task as solving for the angle θ that satisfies the given trigonometric equation, as sin(θ)=1/2 is a conditional equation rather than a universal identity.

2. Determine the reference angle by finding the value in the first quadrant where the sine function equals 1/2

3. Apply the unit circle values to find that sin(30)=1/2 or sin(π/6)=1/2

4. Find the second solution in the interval [0,2*π) by using the property that sine is positive in the second quadrant, calculated as π−π/6=(5*π)/6

5. Generalize the solution by adding integer multiples of 2*π to account for the periodicity of the sine function.

Final Answer

θ=π/6+2*k*π,(5*π)/6+2*k*π

Want more problems? Check here!