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