If cot £ = -9/2 with £ in Quadrant II, find sin £
cot E = -9/12 = X/Y.
r^2 = X^2 + Y^2 = (-9)^2 + 12^2 = 225
r = 15
sin E = Y/r = 12/15.
To find sin £, we need to use the identity tan^2 £ + 1 = sec^2 £.
First, let's find the value of tan £. Since cot £ = -9/2, we know that tan £ is the reciprocal of cot £. So tan £ = -2/9.
Now, we can use the identity tan^2 £ + 1 = sec^2 £ to find sec £. Substituting the value of tan £, we have:
(-2/9)^2 + 1 = sec^2 £
4/81 + 1 = sec^2 £
85/81 = sec^2 £
Since £ is in Quadrant II, sec £ is negative. So sec £ = -(√85/9).
Finally, we can use the identity sec^2 £ - 1 = tan^2 £ to find sin £. Substituting the value of sec £, we have:
(-(√85/9))^2 - 1 = sin^2 £
(85/81) - 1 = sin^2 £
(85 - 81) / 81 = sin^2 £
4/81 = sin^2 £
To obtain sin £, we take the square root of both sides:
sin £ = √(4/81)
Since sin £ is positive, we have:
sin £ = 2/9
Therefore, sin £ equals 2/9.