Remark
pi/4 is between 0 and pi/2 which means that pi/4 is in the first quadrant.
5*pi / 4 is between pi and 3/2 pi which means that the angle is in the third quadrant.
So you are talking about one two angles that are in the first and third quadrants.
Step One
Find the Tangent of pi/4 using the unit circle as a reference.
Since pi/4 is 1/2 way between 0 and pi/2 you are referring to something that has and x value of 0.707 for an x value and 0.707 for a y value. (They are equal)
That is the point where the opposite / adjacent = 0.707/0.707 = 1
Step Two
Find the tangent of 5pi/4 using the unit circle.
Using the same argument as pi/4 this time the opposite / adjacent = -0.707/-0.707 = 1 ( the two minus signs cancel out.)
Answer:
2/9
Step-by-step explanation:
5 dimes and 5 pennies = 10 coins
P( dime) = number of dimes / total
=5/10 = 1/2
keep the dime
4 dimes and 5 pennies = 9 coins
P( penny) = number of penny / total
=4/9
P( dime, keep, penny) = 1/2 * 4/9 = 2/9
50+5x=200
-50 -50
5x=150
divide by 5 on both sides
and your answer is: x=30
Plugging in the given values gives us:
0 = -16t^2 + 80t + 145
This a quadratic equation with two roots. Solving it using using the quadratic formula or by factoring, or by any other solution, the roots are:
6.4531 and -1.4131
We are dealing with time, so we choose the positive root.
Therefore, the answer is 6.4531 seconds