Instructions.
Move the slider slowly and pause at each marked angle. Ask yourself:
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When the angle is \(0^\circ\text{,}\) what shape does the triangle form? What do you notice about the opposite side? What value does the calculator show for \(\sin 0^\circ\text{,}\) \(\cos 0^\circ\text{,}\) and \(\tan 0^\circ\text{?}\) Why might these values make sense from the diagram?
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At \(45^\circ\text{,}\) compare the lengths of the opposite and adjacent sides. What relationship do you observe between them? How does this relate to the values of \(\sin 45^\circ\) and \(\cos 45^\circ\text{?}\) Why do you think this triangle is often called a special triangle?
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As the angle approaches \(90^\circ\text{,}\) how does the triangle change? What happens to the adjacent side? What value is displayed for \(\tan 90^\circ\text{?}\) Why might this value not exist?
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Compare the three angles \(0^\circ\text{,}\) \(45^\circ\text{,}\) and \(90^\circ\text{.}\) What patterns do you notice in the sine values? What patterns do you notice in the cosine values? How are these patterns reflected in the geometry of the triangle?
Discuss your observations with a partner and explain how the diagram supports the calculator values.