Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined".

Question

1) 5π/6

2) 210°

3) 405°

4) -135°

Answer 1

5pi/6 = 150 degrees in quadrant II

reference angle =180-150 = 30 degrees

sin150 = sin30 = 1/2

csc150 = 1/sin150 = 2

cos150 =-cos30 = -sqr3/2

sec150 = 1/cos150 = -2/sqr3 = -2sqr3/3

tan150 = -1/sqr3 = -sqr3/3

cot150 = -sqr3

210 is the same reference angle but in quadrant III

same absolute numerical values but change signs of sines, cosecants, tangents and cotangents

405 -360 = 45

sin405 = sin45 = sqr2/2

csc405 = 1/sin405 = 2/sqr2 = sqr2

cos405 = sqr2/2

sec405 = sqr2

tan405 = 1

cot405 = 1

-135 has refererence angle = 45 degrees, same as with 405, but it's in

quadrant III instead of quadrant I

same absolute value of the numbers, but change the signs for sines, cosecants, cosines and secants