θ is an angle in standard position with terminal side in third quadrant.If cos θ= -3/5, sin θ + cot θ equals

Answer 1

cos θ= -3/5 then sin θ = -4/5.
Note that cosine squared plus sine squared equals 1.

Otherwise assign x = -3 ; r = 5 and observe that y should be negative since the third quadrant requires that x and y should both be negative.
Then x^2 + y^2 = r^2. (-3)^2 + y^2 = 5^2. Choose the negative y. (y = -4)
cos θ= x/r and sin θ = y/r and cot θ = x/y.
Finally, add.

Answer 2

Since cos θ= -3/5, we know we are living in a 3-4-5 right triangle. The fact that the cosine is negative confirms that the terminal side is in the third quadrant.
sin θ = -4/5 because if adjacent / hypotenuse = -3/5, then the opposite side must be 4 (by the pythagorean theorem). It is still negative since both sine and cosine are negative in the third quadrant.
cot θ = cos θ / sin θ = (-3/5) / (-4/5) = 3/4
Thus sin θ + cot θ = -4/5 + 3/4
Putting them both over common denominators:
(-16/20) + (15/20) = -1/20

Answer 3

If cos =3/5, then sin = 4/5 and cot = 4/3. so ans = 32/15.

Answer 4

sin theta=-sqrt(1-(cos theta)^2)=-sqrt(1-9/25)=-4/5
cot theta=cos theta/sin theta=(-3/5)/(-4/5)=3/4
So
sin theta+cot theta=-4/5+3/4=(-16+15)/20=-1/20=-0.05

The fact that theta is in the third quadrant made it possible to determine the sign of sinus.

Answer 5

cos (theta=-3/5)
sin(theta)=-4/5
cot(theta)=+4/3
sin(theta)+cot(theta)=-4/5+4/3 =8/15. answer