If tan θ = 1/√3, what is the value of sin θ?

If tan θ = 1/√3, what is the value of sin θ?

Step 1: Understand that tan θ is the ratio of sin θ to cos θ.
Step 2: Write the equation: tan θ = sin θ / cos θ.
Step 3: Since tan θ = 1/√3, we can set up the equation: sin θ / cos θ = 1/√3.
Step 4: Recognize that in a 30-60-90 triangle, the sides are in the ratio 1:√3:2.
Step 5: In this triangle, the angle opposite the side of length 1 (the shortest side) is 30 degrees.
Step 6: For θ = 30 degrees, sin θ = opposite/hypotenuse = 1/2.
Step 7: Therefore, the value of sin θ is 1/2.

Trigonometric Ratios – Understanding the relationship between sine, cosine, and tangent functions.
Special Triangles – Utilizing the properties of 30-60-90 triangles to find trigonometric values.