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7.1 – Measurement of Angles
Objectives: You should be able to… 1. Convert radians to degrees and vice-versa. 2. Find co-terminal angles.
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*In trigonometry, an angle often represents a rotation about a point.
360 degrees in one revolution.
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Radian Measure of a Central Angle
the number of radius units in the length of its intercepted arc.
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Examples: Give the radian measure of θ if: r = 5 and s = 9
b. r = 8 and s = 10
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*Note: One revolution: degrees = 360° radians = 2π 1 radian =
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Examples: Convert 240˚ to radians. (nearest hundredth)
Convert 1.7 radians to degrees. (tenth) c. Convert radians to degrees.
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Degrees, minutes/seconds
Ex. Convert 12.3º to degrees, min./sec. Ex. Convert 95º10’ to radians.
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When an angle is shown in a coordinate plane, it usually appears in standard position, with its vertex at the origin and its initial ray along the positive x-axis.
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Coterminal Angles 2 angles in standard position, if they have the same terminal ray. There are infinitely many for each terminal ray. *Add or subtract 360° or 2𝜋 from original angle.
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Example: Find two angles, one positive and one negative, that are coterminal with the following angles. 56° b.
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Example: A gear revolves at 40 rpm.
Find the # of degrees per minute through which the gear turns. b. Find the approximate # of radians per minute.
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