Sine and Cosine FunctionsA series of free High School Trigonometry Video Lessons from Brightstorm.
Radian Measure of Angles An angle is the figure formed by two rays with a common endpoint. We typically use degree measures when measuring angles, however we can use radian angle measure as an alternate way of measuring angles in advanced math courses. This measure is based on using a point on the vertex and measuring the arc length compared to the radius.
The Definitions of Sine and Cosine The right triangle definitions of sine and cosine only apply to acute angles, so a more complete definition is needed. The point where the terminal side intersects the unit circle (x, y) is the basis for this definition. Since the radius (and therefore hypotenuse of the right triangle) is 1, the denominators cosine=adjacent/hypotenuse and sine=opposite/hypotenuse are also 1. Thus, the sine definition is y=sine and x=cosine.
Evaluating Sine and Cosine at Special Acute Angles If you want to make your math life incredibly easier, memorize the sine and cosine values for pi/3, pi/4, and pi/6, as well as 0, pi/2, and pi. These values constantly reappear throughout Trigonometry and pre-Calculus problems and proofs. When evaluating sine It is also useful to memorize the conversion from radians to degrees for these values; for example, to remember that pi/6 is equivalent to 30°.
Evaluating Sine and Cosine at Other Special Angles To find the value of sine and cosine at non-acute angles (from 90 to 360), first draw the angle on the unit circle and find the reference angle. A reference angle is formed by the terminal side and the x-axis and will therefore always be acute. When evaluating cosine and sine for the reference angle, determine if each value is positive or negative by identifying the quadrant the terminal side is in.
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