Remaining trig functions tanθ= -2√6/3 and cscθ= >0

Step-by-step explanation:

cot = 1/tan = 1/(-2√6/3) = -3/(2√6) = -√6/4

When the tangent is negative and the cosecant is positive, the angle is in the second quadrant. The cosine and secant are negative there.

sec = -√(1 +tan²) = -√(1 +(-2√6/3)²) = -√(1+24/9) = -√33/3

cos = 1/sec = -3/√33 = -√33/11

sin = tan×cos = (-2√6/3)(-√33/11) = 2√6√33/33 = 2√22/11

csc = 1/sin = 1/(2√22/11) = 11/(2√22) = 11√22/(2·22) = √22/4

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step-by-step explanation:

use that smart brain

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.