Trigonometric Functions

Trigonometric Functions

Trigonometric functions relate the angles of a triangle to the lengths of its sides.

The three primary functions are:

• Sine ($\sin \theta$) = $\frac{\text{Opposite}}{\text{Hypotenuse}}$
• Cosine ($\cos \theta$) = $\frac{\text{Adjacent}}{\text{Hypotenuse}}$
• Tangent ($\tan \theta$) = $\frac{\text{Opposite}}{\text{Adjacent}}$

In the Unit Circle (a circle with radius 1 centered at the origin), these definitions extend to any angle:

• $x = \cos \theta$
• $y = \sin \theta$
• $\tan \theta = \frac{y}{x}$

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Interactive Unit Circle

Drag the slider to change the angle $\theta$ and observe how the sine, cosine, and tangent values change.

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Solved Problems