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Tuesday 9th of August
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 Depdendent Variable

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 Dependent Variable

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# Angles and Degree Measure

An angle has three parts: an initial ray, a terminal ray, and a vertex (the point of intersection of the two rays), as shown in the figure below.

An angle is in standard position if its initial ray coincides with the positive x-axis and its vertex is at the origin. We assume that you are familiar with the degree measure of an angle. It is common practice to use θ (the Greek lowercase theta) to represent both an angle and its measure. Angles between 0Âº and 90Âº are acute, and angles between 90Âº and 180Âº are obtuse.

Positive angles are measured counterclockwise, and negative angles are measured clockwise. For instance, the figure below shows an angle whose measure is -45Âº. You cannot assign a measure to an angle by simply knowing where its initial and terminal rays are located. To measure an angle, you must also know how the terminal ray was revolved. For example, this figure shows that the angle measuring -45Âº has the same terminal ray as the angle measuring 315Âº. Such angles are coterminal. In general, if θ is any angle, then

θ + n(360Âº), n is a nonzero integer

is coterminal with θ.

An angle that is larger than 360Âº is one whose terminal ray has been revolved more than one full revolution counterclockwise, as shown in the following figure.

NOTE

It is common to use the simbol θ to refer to both an angle and its measure. For instance, in the previous figure, you can write the measure of the smaller angle as θ = 45Âº.