the fundamental identities to find the value of the trigonom

the fundamental identities to find the value of the trigonometric function. Find csc theta, given that sin theta = -2/3 and theta is in quadrant IV. 3 Squareroot 7/7 5/4 - Squareroot 7/9 -3/2 Find sin theta, given that cos theta = 4/7 and tan theta

Solution

13) csc (theta) = 1/sin (theta) = 1/ (-2/3) = - 3/2 ,csc is negative in 4th quadrant.

Answere D) -3/2

14) sin(theta)= opposite/hypotenus =(- sqrt_33/7)

(Hypotenus)^2 = (adjacent)^2 +(opposites )^2

49 =( opposite)^2 +16

49-16 =opp^2

Opposite =sqrt_33

Answere is C)

15) cos (theta) = adjacent / hypotenus =(- 12/13)

13^2 = 5^2+adj^2

169 -25= ad^2

Adjacent =12

Answere D) -12/13