Final answer:
The value of sin 36° can be found by expressing it as the sum or difference of two angles. Using trigonometric identities, we can calculate the value of sin 36° as (√2/2)(√(1 - (cos 81°)²) - (√2/2)(√(1 - (√2/2)²)).
Step-by-step explanation:
The value of sin 36° can be found using trigonometric identities and special triangles. Since 36° is not a commonly used angle, we can express it as the sum or difference of two angles that we can work with.
Sin 36° can be written as sin (45° - 9°). Using the identity sin (A - B) = sin A cos B - cos A sin B, we can rewrite this as sin 45° cos 9° - cos 45° sin 9°.
Since sin 45° = cos 45° = √2/2 and sin 9° = cos 81° = √(1 - cos² 81°), we can substitute these values into the expression to find the value of sin 36°.
Therefore, sin 36° is equal to (√2/2)(√(1 - (√(1 - (√2/2)²)²)) - (√2/2)(√(1 - (√2/2)²))).