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Trigonometry

one turn.  If we connect the point P /6 with the center of the circle and drop a perpendicular line from the point P /6 to the x-axis, we get a 30-60-90 triangle. This triangle has hypotenuse length of 1, which is the radius of the circle. So it also has one leg length or the y value of 1/2, and one other leg length or the x value of Ö 3/2. Now we know that the point P /6 has value (Ö 3/2, 1/2). We use the x value of Ö 3/2 divided by the hypotenuse of length 1 and get Ö 3/2, which also is the cos value of the corresponding angle of the x value. Then we do the same thing with the y value and get 1/2, which also is the sin value of the corresponding angle of the y value. Now we can conclude that (x, y) = (cos, sin). So point P /6 and its central angle 30 have cos value of Ö 3/2 and sin value of 1/2. And now we know the cos value of 30 is Ö 3/2 and sin value is 1/2. We can do the same thing with all other points and get the cos values of 0, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, and 360 degrees angles, which are 1, Ö 3/2, 1/2, 0, -1/2, -Ö 3/2, -1, -Ö 3/2, -1/2, 0, 1/2, and Ö 3/2. We can also get all the sin values, which are 0, 1/2, Ö 3/2, 1, Ö 3/2, 1/2, 0, -1/2, -Ö 3/2, -1, -Ö 3/2, and –1/2. These values have brought up the concept of radian. Radian is the measuring value of an angle on the circle. We can find the radian measure by dividing the degree measure of an angle into 180/P . It is very useful to memorize these values because you can use them quickly. Here are some other commonly used values:

 Radian: P /4, 3P /4, 5P /4, 7P /4 Degree: 45, 135, 225, 315 Sine: Ö 2/2, Ö 2/2, -Ö 2/2, -Ö 2/2 Cosine: Ö 2/2, -Ö 2/2, -Ö 2/2, Ö 2/2

The tangent value is the result acquired by dividing the sine value by the cosine value. There are also three other values called the cosecant (csc), secant (sec), and cotangent (cot), which are the inverse of the values sine, cosine, and tangent. Just divide the sine, cosine, and tangent values into 1, and you can get the values for cosecant, secant, and cotangent.

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