Multiply one-digit numbers by three-digit numbers

Learning Objectives Calculate the measure of a coterminal angle by multiplying 360° by a one-digit integer representing the number of rotations. Determine the arc length of a circle by multiplying a three-digit radius by a one-digit central angle in radians. Compute the area of a circular sector where the calculation involves multiplying a three-digit number (derived from the radius squared) by a one-digit central angle. Apply the Law of Sines to find a missing side length when it requires multiplying a three-digit side length by a one-digit scalar. Solve for total angular displacement by multiplying a three-digit angular velocity by a one-digit time interval. Accurately perform the multiplication of a one-digit number by a three-digit number as a critical step within complex...

TermDefinitionExample Coterminal AnglesAngles in standard position (vertex at the origin, initial side on the positive x-axis) that have the same terminal side. They are found by adding or subtracting integer multiples of 360° or 2π radians.An angle of 450° is coterminal with 90° because 450° = 90° + 360° × 1. The multiplication step is 360 × 1. Arc Length (s)The physical distance along the curved line making up an arc. The calculation requires the central angle to be in radians.For a circle with a radius of 150 meters and a central angle of 3 radians, the arc length is s = 150 × 3 = 450 meters. Sector Area (A)The area of the portion of a circle enclosed by two radii and their intercepted arc. The calculation requires the central angle to be in radians.For a circle with a radius of 20 ft...

Coterminal Angle Formula (Degrees) \theta_{coterminal} = \theta + 360^\circ \times n Use this formula to find a coterminal angle, where 'θ' is the given angle and 'n' is an integer representing the number of full rotations. The core multiplication is 360 × n. Arc Length Formula s = r \times \theta Calculates the arc length 's' of a circle with radius 'r' and a central angle 'θ' measured in radians. The core multiplication is r × θ. Sector Area Formula A = \frac{1}{2} r^2 \theta Calculates the area 'A' of a circular sector with radius 'r' and a central angle 'θ' measured in radians. The multiplication often involves a three-digit number (from r²) and a one-digit number (θ).