Step 1: Start with the given information: sin(θ) = 1/√2.
Step 2: Use the Pythagorean identity: sin^2(θ) + cos^2(θ) = 1.
Step 3: Calculate sin^2(θ): (1/√2)^2 = 1/2.
Step 4: Substitute sin^2(θ) into the identity: 1/2 + cos^2(θ) = 1.
Step 5: Rearrange the equation to find cos^2(θ): cos^2(θ) = 1 - 1/2.
Step 6: Simplify the right side: cos^2(θ) = 1/2.
Step 7: Take the square root of both sides to find cos(θ): cos(θ) = ±√(1/2).
Step 8: Simplify √(1/2) to get cos(θ) = ±1/√2.
Trigonometric Identities – Understanding and applying the Pythagorean identity sin²(θ) + cos²(θ) = 1 to find the value of cosine when sine is known.
Quadrants of Trigonometric Functions – Recognizing that the value of cos(θ) can be positive or negative depending on the quadrant in which the angle θ lies.
