This interactive app illustrates how the trigonometry functions – Sine, Cosine and Tangent change with the angle in each quadrant. Use this interactive app to illustrate how the three ratios change with respect to the angle, and why the sign of each of the three functions changes as we vary the angle across different quadrants. More about Sine, Cosine and Tangent in the four quadrants.

## How to Use

Change the angle by:

• dragging your mouse (hold the left mouse button) or your finger around the center in the upper window, or
• dragging your mouse (hold the left mouse button) or your finger horizontally in the lower window.

Note: If you resize your browser, you may have to reload to recalibrate the touch positions.

### Main Panel:

The main panel shows the right angle triangle and the three sides – Hypotenuse, Adjacent and Opposite (see below). The angle used for calculating the trigonometry functions is indicated by a grey shaded arc around the center. The active quadrant is highlighted.

### Graph Panel:

The graph panel shows the three functions vs angle sweep from 0° through 360°. Sine and Cosine graphs are plotted on one set of axes, while tangent is plotted on a separate one due to the asymptotic characteristics at 90° and 270°. This panel can also be used to control the angle (see above). The active angle is highlighted on each graph.

### Side panel:

#### Angle

Angle refers to the primary angle as shown in grey shaded arc at the origin. Angles are rounded to the nearest integer value. The value in radians is rounded to 2 decimal places. The quadrants are number 1 to 4 and are the quadrant where the angle is in is highlighted in pink.

#### Sides

The sides are color coded as the diagram below. The lengths are normalized to the hypothenuse. Hence the hypothenuse is always having a normalized length of 1.0. The side lengths are rounded to two decimal places.

#### Ratios

The three trigonometry functions are calculated based by dividing two of the side lengths. Values are rounded to three decimal places.

• Sine: sin(a) = Opposite / Hypotenuse
• Cosine: cos(a) = Adjacent / Hypotenuse
• Tangent: tan(a) = Opposite / Adjacent