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the point (-2,7)  is located on the terminal arm of<A in standard position.

a) what are the exact primary trigonometric ratios for <A?

b) use a calculator to determine the measures of <A and <B to the nearest degree.
asked Oct 2, 2014 in CALCULUS by anonymous

1 Answer

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(a).

The point  (-2, 7).

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 = - 2 and y = 7 in the above formula, we obtain

r = √[(2)2 + (7)2]

r = √[4 + 49]

r = √53.

Therefore,

sin(A) = y/r = 7/√53.

cos(A) = x/r = - 2/√53.

tan(A) = y/x = 7/(- 2) = - 7/2.

cot(A) = x/y = (- 2)/(7) = - 2/7.

sec(A) = r/x = √53/(- 2) = - √53/2.

csc(A) = r/y = √53/(7) = √53/7.

(b).

The value of sin(A) = - 7/2 -----> A = sin-1(7/√53) ≅ 74.0546o = 74.

One angle C = 90 and remaining angle is B.

The total of three angles in a triangle is 180o.

A + B + C = 180o

74 + B + 90 = 180o.

B + 164 = 180o.

B = 16o.

answered Oct 2, 2014 by casacop Expert

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