Question 884733: Sin cos tan sec csc tan of 225 deggrea
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 225 degrees is equal to 180 + 45 degrees.
reference angle is 45 degrees in quadrant 3.
in quadrant 3, the following properties apply.
sin is negative
cos is negative
tan is positive
csc is negative (reciprocal of sin)
sec is negative (reciprocal of cos)
cot is positive (reciprocal of tan)
if the angle were in quadrant 1, then all functions would be positive.
since the reference angle is 45, then find the functions for 45 degrees as if it were in quadrant 1.
in a 45 degree triangle in quadrant 1:
sin(45) = sqrt(2)/2
cos(45) = sqrt(2)/2
tan(45) = 1
csc(45) = sqrt(2)
sec(45) = sqrt(2)
the functions for 225 degrees are the same as the functions for 45 degrees except that, since the angle is in quadrant 3, the rules for the signs of the functions in quadrant 3 apply and you get:
sin(225) = -sqrt(2)/2
cos(225) = -sqrt(2)/2
tan(225) = 1
csc(225) = -sqrt(2)
sec(225) = -sqrt(2)
you can use your calculator to verify.
the calculator will give you the function in decimal format.
using the calculator, you will get:
sin(45) = .7071....
cos(45) = .7071...
tan(45) = 1
csc(45) = 1/sin(45) = 1.414...
sec(45) = 1/cos(45) = 1.414...
cot(45) = 1
sin(225) = -.7071...
cos(225) = -.7071...
tan(225) = 1
csc(225) = -1.414...
sec(225) = -1.414...
cot(225) = 1
you can verify with your calculator that sqrt(2)/2 = .7071... and sqrt(2) = 1.414...
your solution is:
sin(225) = -sqrt(2)/2
cos(225) = -sqrt(2)/2
tan(225) = 1
csc(225) = -sqrt(2)
sec(225) = -sqrt(2)
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