Our angle, 210° is between 180° and 270° which means it is located in the third quadrant. Sin(x) is only positive for angles in the first and second quadrants, so our answer must be a negative number. Next, we need to determine the reference angle. The reference angle is simply the distance between the given angle and the x-axis. The distance between a third quadrant angle and the x-axis can be calculated by subtracting 180° from the angle. 210° - 180° = 30° sin(210°)= -sin(reference angle) = -sin(30°) = -1/2
Find dy/dx given y=cos(2x)tan(x)
The first thing to determine is which of the rules of differentiation you will need to solve this problem. Since this function contains multiplication, you will use the product rule which states that (f*g)'(x)=f'(x)g(x) + g'(x)f(x). In addition, you will need the chain rule, because you have one function (2x) nested within another function (cos(X)) Let f(x)= cos(2x). Then applying the chain rule gives, f'(x)= -sin(2x)*(2) = -2sin(2x) Let g(x)= tan(x). Then g'(x)= sec^2(x) Now applying the product rule gives dy/dx= -2sin(2x)tan(x) + sec^2(x)cos(2x)
Message More has introduced a new text messaging plan with a $20 monthly fee plus $0.10 per message sent. Your current provider, Wireless World, offers a plan with no monthly fee but charges $0.35 per message sent. You currently send 100 messages per month. Which provider offers you the better deal?
Let X = the number of messages sent Let MM(X) = the amount Message More charges Let WW(X) = the amount Wireless World charges Message More costs $20 per month and $0.10 per message, so MM(X)= 20 + 0.10X Wireless World costs $0.35 per message, so WW(X)= 0.35X Now determine how much each provider will charge you for 100 messages by evaluating each function when X=100 MM(100)= 20 + 0.10(100) MM(100)= 20+ 10 MM(100)= 30 WW(100)= 0.35(100) WW(100)= 35 Since, Message More charges $30 for 100 messages and Wireless World charges $35, Message More would be the better deal.