please help.

Question

consider <A such that cosA= -5/13

a) in which quadrants could this angle exist?

b)if the sin A is negative which quadrant is the angle?

c) sketch a diagram to represent the angle A in standard position, given that the condition in part b) is true

d) write exact expression for the other two primary trigonometric ratios for the angle?

Answer 1

cosA = - 5/13

a) The angle A is exist in second or third quadrant.

 

b) If the sinA is negative

cosA and sinA both are negative then the angle in third quadrant.

 

c) x = 5 , r = 13

From Pythagorean theorem,

r² - x² = y²

y = √(r² - x²)

y = √(13² - 5²)

y = √(169 -25)

y = 12

If the side of an angle A in standard position goes through (-5, -12)

 

Answer 2

Contd..

Angle A is in third quadrant.

x = 5, y = 12

d) Other primary trigonometric ratios are

sin(A) = y/r

sin(A) = -12/13

tan(A) = y/x

tan(A) = 12/5.