Finding the Rule from Images |

In the graph above, the red curve is *y = sin x*. The blue curve is *y = cos x*.

Note that the value of *cos x* can be found by phase shifting the *y = sin x* curve o/2 units left.

Since is **¼ the period**, to assign a cosine rule to a sine function, we simply phase shift

the sine curve **¼ the period** to the left.

Example: if the period is , we perform a phase shift (h + ), then call it cosine.

In the diagrams, you see four sinusoidal curves. Find a sine function rule for each

then perform the correct phase shift to get 4 cosine function rules for the same curves.

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**Solutions**

1) and |
2) and |

3) and |
4) and |

*(all content of the MathRoom Lessons **© Tammy the Tutor; 2004 - ).*