please help.

Question

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.

Answer 1

The coordinate A (-2, 7)

The above coordinate pair in second quadrant.

Angle A is in second quadrant.

x = 2 , y = 7

From pythagorean theorem,

r² = x² + y²

r = √[(2)² + (7)²]

r = √(4 + 49)

r = √53

a) 

Primary trigonometric ratios are

sin(A) = y/r

sin(A) = 7/√53

cos(A) = x/r

cos(A) = -2/√53

tan(A) = y/x

tan(A) = -7/2

 

b)

Find the angle of A:

sinA = 7/√53

= 7/7.28

A = sin ^-1 (0.9615)

A = 74.0576

Sum of the angles in a triangle 180°

We now that <C = 90° and <A = 74.0576°

B = 180° - ( 90° + 74.0576°)

B = 15.9424°

<A = 74.0576° and <B = 15.9424°.