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find the exact values of the 6 trig function for a) 240 degree and b) 13p/4

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2 Answers

Again, such questions can be greatly simplified by remembering that ...

... sin/cos are periodic by 2π (angle α=240 is equivalent to 240-360= -120 while angle β = 8π/4 + 5π/4 = 16π/4 - 3π/4 is equivalent to 5π/4 or to -3π/4) ... while ...

... tan/cot are periodic by π (angle α=240 is equivalent to 240-180= 60 while angle β = 12π/4 + π/4 is equivalent to π/4).

sin 240 = -sqrt3/2

cos 240 = -1/2

tan240 = sqrt3

The other three are the reciprocals of these.

13pi/4  = 3 pi + pi/4. So the reference angle is pi/4. and the angle is in the third quadrant , so

sin 13pi/4 = - sqrt2/2

cos13pi/4 = -sqrt2/2

tan13pi/4 = 1

The other threea re reciprocals of these.