Question 613923: Find the exact value of the trigonometric function. (If an answer does not exist, enter DNE.)
sin 300°
Found 2 solutions by lwsshak3, jsmallt9:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the exact value of the trigonometric function. (If an answer does not exist, enter DNE.)
sin 300°
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Rotate counter-clockwise 300º and you will end up with a reference angle of 60º in quadrant IV where sin<0.
Therefore, sin 300º=-sin60º=-√3/2
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! - If the angle is negative or greater than or equal to 360 degrees then add or subtract 360 until you end up with an angle between 0 and 360.
- Determine where the angle terminates. If it terminates on an axis then the angle is a special angle and you should know its sin, cos, etc. If the angle terminates somewhere else...
- Determine the quadrant where the angle terminates. If the angle terminates in the first quadrant, then the angle is a special angle and you should know its sin, cos, etc. If the angle terminates in a different quadrant...
- Determine the reference angle:
- 2nd quadrant: reference angle = 180 - angle
- 3rd quadrant: reference angle = angle - 180
- 4th quadrant: reference angle = 360 - angle
- If the reference angle is not a special angle, then the original angle was not a special angle and you will need to use your calculator (on the original angle). If the reference angle is a special angle then find its sin, cos, or whatever.
- Determine the sign for the result. Use a positive value unless...:
- 2nd quadrant: cos, sec, tan and cot are negative
- 3rd quadrant: cos, sec, sin and csc are negative
- 4th quadrant: sin, csc, tan and cot are negative
Now let's use this one your problem:
1. Find a co-terminal angle between 0 and 360.
Your angle is already between 0 and 360.
2. Determine if the angle terminates on an axis.
The angles that terminate on the axes are: 0, 90, 180, 270. Your angle is none of these so we continue,
3. Determine where the angle terminates.
Since your angle is greater than 270 and less than 360, it terminates in the 4th quadrant. Since this is not the 1st quadrant, we continue...
4. Determine the reference angle.
Since your angle terminates in the 4th quadrant the reference angle is:
360 - 300 = 60
5. Find the sin, cos, ... for the reference angle.
Since 60 is a special angle, we should know that the sin(60) = 
6. Determine the sign of the result.
Since the angle terminates in the 4th quadrant and since sin is negative in the 4th quadrant:
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