7.1 – Measurement of Angles

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Presentation transcript:

7.1 – Measurement of Angles Objectives: You should be able to… 1. Convert radians to degrees and vice-versa. 2. Find co-terminal angles.

*In trigonometry, an angle often represents a rotation about a point. 360 degrees in one revolution.

Radian Measure of a Central Angle the number of radius units in the length of its intercepted arc.

Examples: Give the radian measure of θ if: r = 5 and s = 9 b. r = 8 and s = 10

*Note: One revolution: degrees = 360° radians = 2π 1 radian =

Examples: Convert 240˚ to radians. (nearest hundredth) Convert 1.7 radians to degrees. (tenth) c. Convert radians to degrees.

Degrees, minutes/seconds Ex. Convert 12.3º to degrees, min./sec. Ex. Convert 95º10’ to radians.

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.

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.

Example: Find two angles, one positive and one negative, that are coterminal with the following angles. 56° b.

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.