if tan theta = -4/3 and sec theta<0 find sin (theta = pi/6). please explain how the answer is derived
Tan theta = y/x
Sec theta = 1/cos theta = r/x
Since Sec is - we know we are in Quadrents 2 or 3. Since Tan is negative, we must be in quadrents 2or4. Combine these... we are in quadrent 2, where x is neg and y is pos, r is pos.
x= -3
y = 4
r^2 = x^2 + y^2
r = root(9 +16)
r = 5
sin theta = y/r = 4/5
not sure where you get sin theta = pi/6... it doesn't. You can even check in your calc because you have tan theta = -4/3, to see what theta is...