**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

Trigonomerty in Basketball.

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.

Trig In Basketball Continued...

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**