Determine the exact values of the six trigonometric functions of the angle.

Question

Assume the point (-2, 10) is on the terminal side of an angle in standard position.

Answer 1

The point is in second quadrant,   so  the cosine, tangent, secant, and cotangent are negative and the sin and cosecant are positive.   The hypotenuse is  sqrt (4 + 100) = sqrt(104) =  2 sqrt(26).   I take the approach of thinking of opp adj and hyp  are being the positive absolute values  (opp = 10, adj = 2, hyp = 2 sqrt(26) ) and using the quadrant rule to determine the signs.     So  

 

sin =  opp/hyp =  10/(2 sqrt(26)) =  5 sqrt(26)/26

csc =  1/sin  =   srtt(26)/5

 

cos =   - adj/hyp = - 2/(2sqrt(26)) = - sqrt(26) / 26

sec = - 1/cos = - sqrt(26)

 

tan = - opp/adj =  - 10/2 = -5

cot = 1/tan  = - 1/5