Find the exact value of cot (theta) for an angle (theta) with sin (theta)= -1/6 and with its terminal side in Quadrant III.

 cotθ = √35 = 5.91

Step-by-step explanation:

Explanation:-

Given sin(θ) = -1/6

We will use trigonometric formula

   co sec ²θ -cot²θ  =1

    cot ² θ =  co sec ²θ - 1  

    cot ² θ =   (-6)² -1 = 36 -1 =35

   cotθ = √35 = 5.91

   Given' θ' is  Quadrant III.

In third quadrant cotθ and tanθ are positive

   cotθ = √35 = 5.91

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)

hello :

by applying the distributive property :

6 × 4.3 = 6 × ( 4 + 0.3 )

            =   (6 ×   4) + (6 ×   0.3)

            = 24 + 1.8

6 × 4.3 = 25.8