The Trigonometric Function: Sin 45° And Its Exact Value

sin 45°

√2/2

sin 45° is a trigonometric function that represents the ratio of the length of the side opposite to the angle of 45 degrees to the length of the hypotenuse of a right triangle. In a right triangle with one angle of 45 degrees, the opposite and adjacent sides are equal in length, and the hypotenuse is √2 times the length of either of these sides.

Using the definition of sine, sin 45° = opposite / hypotenuse = adjacent / hypotenuse = 1 / √2. To simplify this expression, we can multiply the numerator and denominator of the fraction by √2, which gives sin 45° = (1√2) / (√2√2) = √2 / 2.

Therefore, the exact value of sin 45° is √2 / 2, which is an irrational number that cannot be expressed as a finite decimal. However, it is a commonly used value in trigonometry and is equivalent to approximately 0.707.

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