SOLUTION: PLEASE HELP ME SOLVE THIS TRIGONIMETRIC FUNCTIONS: sin 205degree

Question 235574: PLEASE HELP ME SOLVE THIS TRIGONIMETRIC FUNCTIONS:
sin 205degree
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
The values of the Trig. functions for some angles can be found without the use of a calculator (or table). These values are exact and do not involve long decimals. The angles for which exact values can be found easily without a calculator are those that are multiples of 0, 30, and 45 degrees.

205 in not a multiple of 0, 30 0r 45. So we will not be able to find the values of its sin without a calculator. (If you do not have a physical calculator, there is probably a calculator program on your computer which probably knows how to do the Trig. functions.) The only "trick" to using a calculator is to make sure that it is set to angle measures in degrees. (There are other ways to measure angles and some calculators can work with them, too.)

If you have no calculator, then you have to use a table of values for the Trig. functions. You should find one in your Trig. textbook or your teacher should have provided one to those who do not have Trig.-capable calculators. To use the table, you need to know a) the reference angle; and b) the Quadrant of your angle. Since 205 is 25 more than 180, your reference angle is 25 and the angle terminates in the 3rd Quadrant. So look up 25 degrees in the table, find the sin column across from 25 degrees and write down the decimal you see. Then, because sin is negative in the 3rd Quadrant, put a minus sign in front of it.

With or without the calculator, we should get something close to -0.4226 for the sin(205).
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