Solve for t sin(t)=( square root of 3)/2

Problem

sin(t)=√(,3)/2

Solution

1. Identify the reference angle in the first quadrant where the sine function equals √(,3)/2

sin(π/3)=√(,3)/2

2. Determine the quadrants where the sine function is positive. Since √(,3)/2 is positive, t must terminate in Quadrant I or Quadrant II.

Quadrant I:t=π/3

Quadrant II:t=π−π/3=(2*π)/3

3. Account for the periodicity of the sine function, which repeats every 2*π radians.

t=π/3+2*π*k

t=(2*π)/3+2*π*k

4. Define the variable k as any integer to represent all possible solutions.

k∈ℤ

Final Answer

sin(t)=√(,3)/2⇒t=π/3+2*π*k,(2*π)/3+2*π*k

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