tan theta=-4/3 and sec theta<0 find sin (theta=pi/6)

Question

if tan theta = -4/3 and sec theta<0 find sin (theta = pi/6).  please explain how the answer is derived

Answer 1

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...