Multiply one-digit numbers by two-digit numbers

Learning Objectives Apply the multiplication of one-digit by two-digit numbers to scale angles expressed in Degrees, Minutes, Seconds (DMS) format. Calculate the total angular displacement of a rotating object using a one-digit time interval and a two-digit angular velocity. Determine the resulting angle and its primary coterminal angle after multiplying a two-digit angle measure by a one-digit scalar. Compute the arc length of a sector where either the radius or the angle (in radians) is a one-digit number and the other is a two-digit number. Evaluate trigonometric functions for angles that are the product of a one-digit integer and a two-digit base angle. Convert between DMS and decimal degree representations for scaled angles. How many full rotations does a vinyl record s...

TermDefinitionExample Angular Displacement (θ)The change in the angular position of a rotating object, measured in degrees, radians, or revolutions.If a wheel turns from a 0° position to a 90° position, its angular displacement is 90° or π/2 radians. Degrees, Minutes, Seconds (DMS)A system for subdividing a degree into smaller parts for precision. One degree (°) is equal to 60 minutes ('), and one minute is equal to 60 seconds (").The angle 45.51° can be expressed as 45° 30' 36". Angular Velocity (ω)The rate at which an object rotates, typically measured in radians per second (rad/s) or revolutions per minute (RPM).A fan spinning at 30 rad/s completes 30 radians of rotation every second. Coterminal AnglesAngles in standard position that have the same terminal side. The...

DMS Multiplication k \cdot (D° M' S") = (k \cdot D)° (k \cdot M)' (k \cdot S") To multiply an angle in DMS form by a scalar k, multiply each component (degrees, minutes, seconds) by k independently. Then, regroup by carrying over any values where seconds or minutes exceed 59. Total Angular Displacement \theta_{total} = \omega \cdot t The total angular displacement (θ) is the product of the constant angular velocity (ω) and the time interval (t). Ensure units are consistent before multiplying. Arc Length Formula s = r \cdot \theta The arc length (s) of a circle sector is the product of the circle's radius (r) and the subtended central angle (θ). The angle θ MUST be in radians for this formula to be valid.