Question

Find sin(π/4). Round to 3 decimal places.

Answer 1

Explanation:

sin (pi/4) = sqrt(2) / 2 = .707

you either just know this after a time or you can use a calculator (in RADIAN mode)

Answer 2

sin(π/4) = sin(45°) = 0.707106781186548 ≈ 0.707 (rounded to 3 decimal places)

Explanation:

here are the steps:

Convert π/4 to degrees: π/4 * (180/π) = 45°

• Use the definition of sine to find the sine of 45°:

sin(45°) = opposite/hypotenuse

• In a right-angled triangle with an angle of 45°, the opposite and adjacent sides are equal, so we have:

sin(45°) = opposite/hypotenuse = adjacent/hypotenuse = 1/√2

• Rationalize the denominator by multiplying both the numerator and denominator by √2:

sin(45°) = 1/√2 * √2/√2 = √2/2

• Round to 3 decimal places: sin(45°) ≈ 0.707

Therefore, sin(π/4) = sin(45°) = √2/2 ≈ 0.707 (rounded to 3 decimal places).