Matt Wolf - Central Bucks School District



|Learning Goals: |At the completion of the lesson, you will be able to… |

| |Evaluate limits of trigonometric functions |

| |Evaluate infinite limits of trigonometric functions |

Basic Trigonometric Limits:

[pic] [pic]

Rules for Trigonometric Limits (only work for sin or tan not cos):

Infinite Trigonometric Function Limits

Recall that the graphs of the functions sinx and cosx oscillate between [-1, 1] as [pic].

Therefore, when we evaluate infinite limits of trigonometric functions, we can assume that terms of sinx and cosx are limited to values between [-1, 1].

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[pic] [pic] [pic]

Example: [pic] Example: [pic] Example: [pic]

To evaluate trigonometric function limits, we want to isolate a term in the form of one of the above rules:

[pic] [pic] [pic]

Note – these rules work for sin and tan but not cos

|Method 1 |Substitution |[pic] |

|Method 2 |Convert to |[pic] |

| |Sines/Cosines | |

|Method 3 |Factoring |[pic]"[pic] |

|Method 4 |Separate Fractions |[pic] |

Method 5Change of Variable[pic] Hint: Let ∙[pic]Method 4Separate Fractions[pic]

|Method 5 |Change of Variable |[pic] Hint: Let [pic]so if [pic]then [pic] |

[pic]

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[pic] [pic]

Let [pic]so if [pic]then [pic]

[pic] [pic]

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