1 If tan 125 and is in quadrant IV find the values of the re

1. If tan =-12/5 and is in quadrant IV, find the values of the remaining trigonometric functions of 2. If cos -5 and 0

Let = P = Perpendicular

B = Base

H = Hypotenuse

1) tan = -12/5 = P/B

Here P = 12, B = 5 ======> H = sqrt(12^2 + 5^2) = 13

Then

Sin = P/H = -12/13

Cos = B/H = 5/13

Csc = 1/sin = -13/12

Sec = 1/cos = 13/5

Cot = 1/tan = -5/12

2) cos = -4/5 = B/H

Here B = 4, H = 5 ======> P = sqrt(5^2 - 4^2) = 3

Then

Sin = P/H = 3/5

tan = P/A = -3/4

Csc = 1/sin = 5/3

Sec = 1/cos = -5/4

Cot = 1/tan = -4/3

3) sin = 1/6 = P/H

Here P = 1, H = 6 ======> B = sqrt(6^2 - 1^2) = sqrt(35)

Then

cos = B/H = -sqrt(35)/6

tan = P/A = -1/sqrt(35)

Csc = 1/sin = 6

Sec = 1/cos = -6/sqrt(35)

Cot = 1/tan = - sqrt(35)

4) tan = 2/3 = P/B

Here P = 2, B = 3 ======> H = sqrt(2^2 + 3^2) = sqrt(13)

Then

Sin = P/H = -2/sqrt(13)

Cos = B/H = -3/sqrt(13)

Csc = 1/sin = - sqrt(13)/2

Sec = 1/cos = - sqrt(13)/3

Cot = 1/tan = 3/2