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Unit Circle to Sine and Cosine Functions (Taylor Edit)

Creation of this resource was inspired by this resource and this resource created by Anthony Or. Slide the slider first. Explore!

Sine Function

How is the Unit Circle being used in order to create the sine function? Think about both the x and y values.

Why is the vertical distance used for sine?

Cosine Function

How is the Unit Circle being used in order to create the cosine function? Think about both the x and y values.

Why is the vertical distance used for cosine?

Tangent Function

How could we take what we know about sine and cosine and apply it to help us graph tangent?

What happens to the tangent function when sine and cosine are a value of zero?

Secant and Cosecant Functions

We will be exploring secant and cosecant later today, but will get started now. Secant is the reciprocal of cosine (1/cos(x)). Cosecant is the reciprocal is sine (1/sin(x)). How could you apply this information to form the secant and cosecant graphs? Think about what 1/a changing value means. What's the domain? Explain some of the features of the graph you may see. This may include detailed written conjecture or a sketch of your hypothesized graph. If you sketch, write that you did, and attach it in the GC assignment.