### Trigonometry Golf

This 9-hole minigolf game helps you practise using the pythagorean theorem, trigonometry and the unit circle, depending on the game mode.

Click on the image to the right to open the game.

### How to play

To take a shot, you will need to enter the required angle and distance. Clicking where you want to hit the ball to will bring up a hint (see left). Depending on the mode, some information will be given to you, leaving some unanswered questions for you to solve with your own calculations.

The game is in degrees by default, but radians may be selected from the pause menu (escape).

### Game Modes

There are six game modes covering different skills and offering various degrees (pun not intended) of difficulty. The game automatically starts in * bearings* mode, and can be changed by clicking on the

*button.*

**new game**
** Bearings:** estimate the three-figure bearing of each shot.

** Pythagoras:** calculate the required distance (hypotenuse) with the Pythagorean theorem.

** Trig side lengths**: use sine and cosine to calculate the distance (hypotenuse) of each shot.

** Trig angles:** use inverse sine, cosine or tangent to calculate the angle of each shot.

** Challenge**: calculate both the distance (hypotenuse) and angle of shot using trigonometry (the pythagorean theorem could also be used for the distance).

** Unit circle:** gain familiarity with the unit circle and use its properties to calculate the angle of each shot.

**In the unit circle, the sin of the central angle is equal to the y axis and the cosine is equal to the x axis. Use your common sense, as each angle could represent two possibe directions.**

*Hint:*### Extension: A Puzzling Problem

If you played the unit circle game mode, you probably saw that the length of the longest axis (x or y) of your triangle is given in the hints. This is shown instead of the shortest side as there is usually more space to display it clearly.

Click around the screen and notice how the values change. Did you notice that for angles near an axis, the distance display changes from two decimal places to three? Why is this necessary?