Question 415283: Using reference agnles, how do I find the exact values of
1) sec 240 degrees=
2) tan 9pi/2=
3) cot 13pi/3=
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Using reference agnles, how do I find the exact values of
1) sec 240 degrees=
2) tan 9pi/2=
3) cot 13pi/3=
..
The problem here is to find the reference angle and the quadrant it is in. The reference angle is the angle the terminal side makes with the x-axis.
1) Sec 240 degrees:Starting from the initial side, rotate counter-clockwise 180 deg, then another 60 deg. The reference angle is 60 deg located in quadrant III. In this quadrant the cos is negative, so the sec is negative. Cos 60 deg = -1/2, so its reciprocal,sec 60 deg=-2.
12) tan 9pi/2: 5 rotate counter-clockwise 4pi then another 1/2 pi, which make the reference angle pi/2,sin=1 and cos=0, so tan function is undefined at this reference angle.
3)cot 13pi/3: This is 4+1/3 pi, which makes the reference angle=60 deg.located in quadrant I.
Cot 60 = Sqrt(3)/2
ans:
1)Sec 240 deg=-2
2)tan 9pi/2=undefined
3)cot 13pi/3=Sqrt(3)/2
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