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Trigonometry In Sports

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on 24 October 2014

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Transcript of Trigonometry In Sports

Trigonometry In Sports
Trig In Soccer Continued...
This video shows a short demonstration of trigonometry in soccer.
Trigonometry in Football.
Trigonometry in Baseball.
Background Knowledge on Trigonometry.
The Six Trig Functions: Sin, Cos, Tan, Sec, Csc and Cot.
Pythagorean Theorem: A^2 + B^2 = C^2

Trigonometry applies to how the player aims and throws the ball the shoot. Most players attempt to shoot at a 45 degree angle.

Example: Find the range of the ball to make it at a 45 degree angle.
Formula for range: Vo^2sin(2a)/32
A= 45
Vo^2sin(2*45)/32
=Vo^2/32
Applied to a 3 pont shot which is 25 ft. away:
25=Vo^2/32
Vo^2=800
Vo=28.2843
Conclusion:
To make a 3 point shot the player must throw the ball at approximately 28 ft. per secon and 19 mph.
2 minute video of trigonometry in basketball.
Trigonometry in Soccer.
Trigonometry helps determine the angle at which to kick the ball depending upon the height o the goal.

Example 1: At what angle would you kick a soccer ball to hit the cross bar thats 2.666 yards high?
12 yards out:
12^2+2.666^2= 12.293 yards
sin^-1 2.666/12.293
= 12.53 degress
18 yards out:
18^2+2.666^2 = 18.196 yards
sin^-1 2.666/18.196
= 8.43 degrees
22 yards out:
22^2=2.666^2 = 22.161 yards
sin^-1 2.666/22.16
= 6.91 degrees
Trigonometry in Golf

Golf applies to trigonometry because the golfer needs to
determine a specific angle to ensure the ball reaches its
final destination.

Example: A golf player wanted to know how he could get the ball in the put hole n the least amount of tries.
Find angle A (TanA = opposite/adjacent)
5.2/8.5= Tan^-1(0.611) = 31.4
Find Angle B (Pythagorean Theorem)
18.5^2+10.5^2 = square root of 452.5
=21.27
Last Angle (SinC= opposite/hypotenuse)
18.5/21.27=sin^-1(0.869) = 60.4 degrees

Trigonometry applies a great deal to football especially when the ball is being kicked or thrown. It could help explain the distance the football travels.

Example: The football is kicked by the player at the velocity of 250m/s with the initial angle of 60 degrees. What is the range covered by the football?
25.0*cos(60)= 12.5 m/sec
Trigonometry helps determine the angle that the player shoul swing his bat. It also tellyou the distances between plates.

Example: *Using the picture* Is first base closer to home plate or second base?
The distance from home plate to first base and first base to second is 90'. Therefore 127.28 ft.- 60.5 ft. is 66.78 ft. making it closer to home plate.
1st Period: Candis, Edwin, Thalia, and Derrick
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