How was this solved, please show work The point P = (20, -15) on the circle x^2

Question

How was this solved, please show work

The point P = (20, -15) on the circle x^2 + y^2 = r^2 is also on the terminal side of an angle theta in standard position. Find sin theta, cos theta, tan theta, csc theta, sec theta, and cot theta. sin theta = -3/5 (Type an integer or a simplified fraction). cos theta = 4/5 (Type an integer or a simplified fraction.) tan theta = -3/5 (Type an integer or a simplified fraction.) csc theta = -5/3 (Type an integer or a simplified fraction.) sec theta = 5/4 (Type an integer or a simplified fraction). cot theta = -4/3 (Type an integer or a simplified fraction.)

Explanation / Answer

here equation of circle is r2 = x2 + y2

P(20, -15)

So if we put the value of x = 20 and y = -15 we can get r = (400+225)1/2 = 25

So we can get values of trignometric function Sin O = perpendicular / hypotenuse = y / r = -15/25 = -3/5

Cos O = Base / hypotenuse = x / r = 20 / 25 = 4/5

Tan O = perpendicular / base = y / x = -15/20 = -3/4

Cosec O = 1 / Sin O = -5/3

Sec O = 1/Cos O = 5/4

Cot O = 1/Tan O = -4/3

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