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Lecture

radian measures.docx

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Department
Mathematics
Course
MATA30H3
Professor
Ken Butler
Semester
Winter

Description
Radian Measure  Angle X is defined as the length, a, the arc that extends the angle divided by the radius, r, of the circle: X = a/r.  2 Pi rad = 360 degrees or Pi rad = 180 degrees.  To convert degrees to radians, multiply degree measure with Pi/180.  To convert radian measure to degrees, multiply radian measure with 180/Pi. Trigonometric ratios and special angles  You can use a calculator to calculate trigonometric ratios for an angle expressed in radian measure by setting the angle mode to radians.  You can determine the reciprocal trigonometric ratios for an angle expressed in radian measure by first calculating the primary trigonometric ratios then using the reciprocal key on the calculator.  You can also use the unit circle and special triangles to determine exact values for the trigonometric ratios of the special angles 0, Pi/6, Pi/3. Pi/4, and Pi/2.  You can use the unit circle along with the CAST rule to determine exact values for the trigonometric ratios of multiples of the special angles. Equivalent Trigonometric Expressions  You can use a right triangle to derive equivalent trigonometric expressions that form the cofunction identities, such as sinx = cos(Pi/2 – x).  You can use the unit circle along with transformations to derive equivalent trigonometric expressions that form other trigonometric identities, such as cos(Pi/2 + X) = -sinx  Given a trigonometric expression of a known angle, you can use the equivalent trigonometric expressions to evaluate trigonometric expressions of other angles.  You can use graphing technology to demonstrate that two trigonometric expressions
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