Please help!

Question

The point A(3,-7) is on the terminal arm of an angle. Determine exact expression for the primary trigonometric ratios gor the angle. Including sketch

Answer 1

The coordinate A (3, -7)

The above coordinate pair in fourth quadrant.

Angle A is in fourth quadrant.

From pythagorean theorem,

r² = x² + y²

r = √[3² + (-7)²]

r = √(9 + 49)

r = √58

sin(A) = y/r

sin(A) = -7/√58

cos(A) = x/r

cos(A) = 3/√58

tan(A) = y/x

tan(A) = - 7/3

cot(A) = x/y

cot(A) = -3/7

sec(A) = r/x

sec(A) = √58/3

csc(A) = r/y

csc(A) = - √58/7