Pythagorean Trigonometric Identity (1)
This applet shows the derivation of one of the most frequently used trigonometric identities. [br][br]How, specifically, does it relate to the Pythagorean Theorem?
Limits: Introductory Questions
The questions you need to answer are contained in the applet below.
[b][color=#1e84cc]Recall that VELOCITY is a vector quantity (quantity having both MAGNITUDE and DIRECTION). [br][/color][color=#980000]SPEED, on the other hand = | VELOCITY |, thus always making it a non-negative quantity.[/color][/b][br][br]Thus, there are times when velocity can be [color=#cc0000]negative.[/color] [br][br]The following graph and table provides information with respect to a person driving away from home.[br]Let [i]t [/i]= the number of hours that have passed. [br]Let [i]d[/i] = this person's displacement from home. [br][br]Study the graph and table carefully. (They display the same information.) [br]Then, answer the questions that appear below the applet.
What was the average velocity for the first half hour of your trip?
What was your average velocity from t = 0.5 hr to t = 1 hr?
What was your average velocity between t = 1.5 hrs to t = 2 hrs?[br]Explain what your answer physically means with respect to the context of this story.
-40 mi/hr. This simply means you were driving at an average speed of 40 mi/hr while heading in the OPPOSITE DIRECTION. (Your displacement here is negative.)
What was your average velocity for the entire trip? (Assume your trip took 2.5 hours.)
Between what two listed 1/2-hr increments was your [b]average speed[/b] the greatest?
Between t = 2 hrs. and t = 2.5 hrs. [br]Average speed = | average velocity | = | 120 mi/hr | = 120 mi/hr