Question 1002716: hello, if I could have help with a problem.
I was a bit confused on this one.
question: find exact values of 6 trig function of angle 1575 degrees
so what I have done so far was I subtracted 1575 - 360 till I got a number in the unit circle. now when I did this I got 165.
Thank you
Found 3 solutions by person24, lwsshak3, MathTherapy:
Answer by person24(13)   (Show Source):
You can put this solution on YOUR website! The 6 trig functions are sin,cos,tan,csc,sec,and cot.
To find those we need to convert 1575 degrees into a standard angle that is more friendly to work with.
1575 x(pi/180 degrees)
35pi/4 radians
after counting where that is on the unit circle it lies on the same point as 3pi/4 does
3pi/4 has a slope (tangent) of -1
that means tanx=-1
since tangent is opposite over adjacent and 3pi/4 is in the second quadrant we know that
opposite=-1 (since cosine in the second quadrant is negative)
and
adjacent=1
now we can use the Pythagorean theorem to find the hypotenuse. a^2+b^2=c^2
1^2+-1^2=c^2
1+1=c^2
2=c^2
sqrt2=hyptoneuse
now we can use that to figure out the rest of the function
since cot is the inverse of tan we know that
cotx=-1
sine is opposite over hypotenuse so
sinx=1/sqrt2.... ooo but sqrt in the bottom is claimed to be evil of some sort
so lets mutpily the top and bottom by sqrt2 since it is a value of 1
sqrt2/2
sinx=sqrt2/2
and csc is the inverse of sine so
cscx=sqrt2
cosine is adjacent over hypotenuse so
cosx=-sqrt2/2... already mutiplied by sqrt2/sqrt2 remember because sqrt on bottom is evil....
inverse of cosine is sec
secx=-sqrt2
okay lets review...
secx=-sqrt2, cscx=sqrt2, cosx=-sqrt2/2, sinx=sqrt2/2, cotx=-1, tanx=1
hope that helps! :)
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! find exact values of 6 trig function of angle 1575 degrees
Subtract 360 from 1575as many times as needed until you get an answer ≤ 360
1575-360=1215-360=855-360=495-360=135 deg
This is a reference angle of 45 deg in quadrant II in which sin>0, cos<0, tan>0
exact values of 6 trig function of angle 1575 degrees:
sin 45 =√2/2
cos 45 =-√2/2
tan 45=1
csc 45=√2
sec 45=-√2
tan 45=-1
alternate method: divide1575 by 360=1575/360=4.375
then subtract 1the whole number*360 from 1575 to get an angle ≤ 360 deg
1575-4*360=135 deg
Answer by MathTherapy(10555)  (Show Source):
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