An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t), so it's location at time t is P(t)=(cos(t),sin(t)) . Assume 0 < t < π/2. At a given time t, the tangent line to the unit circle at the position P(t) will determine a right triangle in the first quadrant. (Connect the origin with the y-intercept and x-intercept of the tangent line.) The identity
sin(2t)=2sin(t)cost(t)
might be useful in some parts of this question.

Brook states that the distance on the line is 4 units. caleb states that the whole line does not have a distance because it continues on forever. vivian states that the line is 6 units long. which distance did brook measure? which distance did vivian measure?

You give a $4 tip for a meal that cost $22. approximately what percent of the bill was your tip?

Michelle and julie work at a catering company. they need to bake 264 cookies for a birthday party that starts in a little over an hour and a half. each tube of cookie dough claims to make 36 cookies, but michelle eats about 1/5 of every tube and julie makes cookies that are 1.5 times as large as the recommended cookie size.it takes about 8 minutes to bake a container of cookies, but since julie's cookies are larger, they take 12 minutes to bake. a. how many tubes should each girl plan to bake? how long does each girl use the oven? b. explain your solution process what did you make? c. what assumptions did you make?