today im going to show you how to find refernce angles with other trig functions. in 7-4 we learned how to do this with sin and cos which was fairly easy. today is differnt. today will be showed how to do it with tan cot sec and csc. steps 1 and 3 are the same. step 2 however is slightly differnt. insted of y/r for sin and x/r for cos, now we have to do y/x for tan and x/y for cot to find out if its positive or negative. we also have r/y for csc and r/x for sec. it is not much differnt but it could get tricky.
EX:
a) tan 123 degrees
1) it is b/w 90 and 180 degrees so it is the second quadrant
2) it is negative because it is y/x. y is positive and x is negative making it a negative tan.
3) 123-180=-57 |-57|= 57
refernce angle is -tan 57
b) cot 310 degrees
1) it is b/w 270 and 360 degrees making it in the 4th quadrant.
2) it is negative because it is x/y. y is negative and x is negative making it a negative cot.
3) 310-360=-50 |-50|=50
refernce angle is -cot 50
c) csc -300 degrees
1) -300 is in 1st quadrant because you go backwards 300 degrees in the unit circle
2) it is positive because it it r/y. r is positive and y is positive making it a positive csc.
3)-300+360= 60
reference angle is csc 60
d) sec 245
1) it is b/w 180 and 270 making it in the 3rd quadrant.
2) it is negative because it is r/x. r is positive and x is negative making it a negative sec.
3) 245-180= 65
reference angle is -sec 65
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