If cos(θ) = 1/2, what is the value of sin(θ)?

If cos(θ) = 1/2, what is the value of sin(θ)?

Step 1: Start with the given value of cos(θ), which is 1/2.
Step 2: Use the Pythagorean identity, which states that sin^2(θ) + cos^2(θ) = 1.
Step 3: Substitute the value of cos(θ) into the identity: sin^2(θ) + (1/2)^2 = 1.
Step 4: Calculate (1/2)^2, which is 1/4.
Step 5: Rewrite the equation: sin^2(θ) + 1/4 = 1.
Step 6: To isolate sin^2(θ), subtract 1/4 from both sides: sin^2(θ) = 1 - 1/4.
Step 7: Calculate 1 - 1/4, which equals 3/4.
Step 8: Now we have sin^2(θ) = 3/4.
Step 9: To find sin(θ), take the square root of both sides: sin(θ) = ±√(3/4).
Step 10: Simplify √(3/4) to get sin(θ) = ±√3/2.

Trigonometric Identities – Understanding and applying the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 to find the sine value from the cosine value.
Quadrants of Trigonometric Functions – Recognizing that the sine function can be positive or negative depending on the angle's quadrant.