Tan(theta)= -1 part1. write an equation that expresses the value of theta in terms of an appropriate inverse trigonometric expression part2. on the interval [0,2pi], what values of theta satisfy your equation in part 1? part3. write an expression for all solutions to the equation

we are given

(I)

Since, we have to solve for theta

so, we will take tan^-1 both sides

we can cancel tan with tan^-1

we get

(II)

we can use unit circle

we know that

tan is negative in second and fourth quadrant

so, we get

(III)

We know that time period of tan is pi

It means after pi , it repeats itself

so, we can add pi*k to get general solution

where k can be any integers

so, our solution is

.................Answer

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.