Find sin(u/2) if tan(u)=-7.721 and u is in quadrant 4

.6601

Step-by-step explanation:

to find u, which we assume is an angle of course, we can take arctan of both sides.  so arctan(-7.721) = -1.4420.  this angle is in quadrant 4, but it is not in the range.  In this instance you just go around the circle again, or add 2pi, which gets us 4.8412.  You can check and you get the same answer if you take the tangent of either.

So now we have a number in the appropriate range  in the appropriate quadrant.  That means we have the correct angle.  The question asks what is sine of that angle cut in half.  so sin(4.8412/2), which gets you your answer.  let em know if something didn't make sense.  

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

the answer is the option b

the range is all real numbers

step-by-step explanation:

we know that

the absolute value parent function is equal to

see the attached figure to better understand the problem

so

a. it is v-shaped > is true

b. the range is all real numbers > is not true

because the range is the > [0,∞)

all real numbers greater than or equal to zero

c. it goes through the origin > is true

d. the domain is all real numbers > is true

step-by-step explanation: