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GeoGebraClasse GeoGebra

Unit Circle Trigonometry

Drag the slider for to adjust the angle. Notice the coordinates of point on the unit circle. On the applet below, you have as a reference angle, which is an angle between 0º and 90º.

Unit circle

The first quadrant

We consider the first quadrant as the space between 0º and 90º.

Angles in the first quadrant

1. Choose two angles in the first quadrant and register the value for their sine and cosine. 2. For each angle, calculate the sine and cosine of their reference angle. 2. Compare those values.

The second quadrant

We consider the second quadrant as the space between 90º and 180º.

Reference angles and the second quadrant.

Choose two angles and register their values. What pattern do you see between the values of the angles chosen and their reference angles?

Second quadrant angles conversion in algebra

Write down the relation you found in the previous question using math notation.

Angles in the second quadrant

1. Choose two angles in the second quadrant and register their value for their sine and cosine. 2. For each angle, calculate the sine and cosine of their reference angle. 3. Compare those values.

The third quadrant

We consider the third quadrant as the space between 180º and 270º.

Reference angles and the third quadrant

Choose two angles and register their values. What pattern do you see between the values of the angles chosen and their reference angles?

Third quadrant conversion in algebra

Write down the relation you found in the previous question using math notation.

Angles in the third quadrant

1. Choose two angles in the second quadrant and register their value for their sine and cosine. 2. For each angle, calculate the sine and cosine of their reference angle. 3. Compare those values.

The fourth quadrant

We consider the third quadrant as the space between 270º and 360º.

Reference angles and the fourth quadrant

Choose two angles and register their values. What pattern do you see between the values of the angles chosen and their reference angles?

Fourth quadrant conversion in algebra

Write down the relation you found in the previous question using math notation.

Angles in the fourth quadrant

1. Choose two angles in the second quadrant and register their values for their sine and cosine. 2. For each angle, calculate the sine and cosine of their reference angle. 3. Compare those values.