How do you find the exact value of the trigonometric function cos 570 degrees?

2 Answers
Apr 19, 2015

There exists 4 trigonometric quadrants. All, Sine, Tan & Cos .

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570 degrees turns out to land in the tan quadrant, therefore cos(570) has to be negative.

90 (all) + 90 (sin) + 90 (tan) + 90 (cos) + 90 (all) + 90 (sin) + 30 (tan) makes 570 degrees and the last turn helps us land in the tan quadrant.

Remember that 90+90+90+90+90+90+30=570.

So we have to create a 30 degree right angled triangle in the tan quadrant.

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We then figure out the value of the adjacent side to this triangle and its hypotenuse to get the value of cos(570) which is equal to #-sqrt(3)/2#

Use the trig unit circle as proof.
#cos 570^o = cos (360^o + 210^o) = cos (0^o + 210^o) = cos (180^o + 30^o)#

#cos(180^o + 30^o) = cos(180^o)cos(30^o) - sin(180^o)sin(30^o)#
#= -1*sqrt(3)/2 - 0*1/2#

= #sqrt(3)/2#

or...

#cos 570^o = cos (360^o + 210^o) = cos (0^o + 210^o)#
# = cos (210^o) = sqrt(3)/2#