Answer:
+/- 3/5
Step-by-step explanation:
[tex]\text{csc}(\theta)[/tex] = 1 1/4 Convert 1 1/4 into an improper fraction
[tex]\text{csc}(\theta)=\dfrac{5}{4}[/tex] Turn 5/4 upsidedown to get sin( sin[tex]\theta[/tex])
[tex]\dfrac{1}{csc(\theta)} =sin(\theta)\\[/tex] 1 / csc(theta) = sin(theta)
[tex]sin(\theta) = 4/5[/tex] sin(theta) = 4/5 which is the reciprocal of 5/4
Cos(theta) = sqrt(1 - sin^2(theta) ) This is the identity relationship between sin(theta) and cos(theta)
Cos(theta) = sqrt( 1 - (4/5)^2 ) (4/5)^2 = 16/25; 1 - 16/25 = 9/25
Cos(theta) = sqrt( 9/25)
Cos(theta) = +/- sqrt(9/25) sqrt of 9/25 = 3/5
cos(theta) = +/- 3/5 Answer <<<<
