math20

Question

the point A (-3,-5) is on the terminal arm of an angle. Determine exact expeession for the primary trigonometric ratios for the angle. Including sketch

Answer 1

The point  A = (-3, -5).

Let A be an angle in standard position with (x, y) a point on the terminal side of A and r = √(x² + y²) ≠ 0.

To find the value of r, substitute x = - 3 and y = - 5 in the above formula, we obtain

r = √[(-3)² + (-5)²]

^{r = √[9 + 25]}

r = √34.

Therefore,

sin(A) = y/r = - 5/√34.

cos(A) = x/r = - 3/√34.

tan(A) = y/x = (- 5)/(- 3) = 5/3.

cot(A) = x/y = (- 3)/(- 5) = 3/5.

sec(A) = r/x = √34/(- 3) = - √34/3.

csc(A) = r/y = √34/(- 5) = - √34/5.

Graph :