Cot-1(-radical3)
find exact value in radians

θ = 5π/6  or 11π/6

Step-by-step explanation:

It is required to find the value of  

Let  

So, cot θ = -√3 ⇒ tan θ = 1/cot θ = -1/√3

So, from the basic angles, we should know that

tan 30 = 1/√3 ⇒ Cot 30 = √3

But the given cot function is negative, so the required angle lies at the second quarter or at the fourth quarter.

So,  θ = -30°

OR  θ = 330°  or 150°

converting to radians by multiplying at π/180

∴ θ = 330 * π/180 = 11π/6

Or θ = 150 * π/180 = 5π/6

So, θ = 5π/6  or 11π/6

x = number of messages sent or received

y = total cost per month

Plan A costs $30 per month plus $0.10 per text message. So the cost for plan A is y = 0.10*x + 30. The portion 0.10*x represents just the cost of the 10 cents per message, and then we add on the fixed cost of $30 to get the total cost.

In a similar fashion, plan B's cost is y = 60. There is no cost per message, so we don't have to include x in the picture. The cost is a flat fee, which leads to a flat horizontal line graph (as shown in the attachment below)

Our two equations are: y = 0.10x+30 and y = 60. Let's use substitution to find x

y = 0.10x + 30

60 = 0.10x + 30 ... replace y with 60 (works because y = 60)

60-30 = 0.10x

30 = 0.10x

0.10x = 30

x = 30/0.10

x = 300

If you send or receive 300 messages, then both plans will cost the same. We can see this on the graph below where the two lines cross at (300,60). Note how plugging x = 300 into the first equation simplifies to y = 60.