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Madeira Precalculus Blog

Welcome to Mr. Corn’s blog for Precalculus and Math 181. Here you’ll find student reviews of what’s going on in Precalculus and other helpful information about precalculus.

Tuesday, March 16, 2010

Precalculus 3/16/10

Using Trig Identities-Day 1

An identity is true for all numbers
An equation is true for some numbers

Trig Identities

$csc\theta=\frac{1}{sin\theta}$

$sec\theta=\frac{1}{cos\theta}$

$cot\theta=\frac{1}{tan\theta}$

$tan\theta=\frac{sin\theta}{cos\theta}$

$cot\theta=\frac{cos\theta}{sin\theta}$

$sin(-\theta)=-sin\theta$

$cos(-\theta)=cos\theta$

$tan(-\theta)=-tan\theta$

$csc(-\theta)=-csc\theta$

$sec(-\theta)=sec\theta$

$cot(-\theta)=-cot\theta$

$cos^2\theta+sin^2\theta=1$

$sin^2\theta=1-cos^2\theta$

$cos^2\theta=1-sin^2\theta$

$1+tan^2\theta=sec^2\theta$

$tan^2\theta=sec^2\theta-1$

$1=sec^2\theta-tan^2\theta$

$cot^2\theta+1=csc^2\theta$

$1+cot^2\theta=csc^2\theta$

$1=csc^2\theta-cot^2\theta$

$cot^2\theta=csc^2\theta-1$

Proving Identities

HELPFUL HINT-Work with the most complicated side!

$sec\theta*sin\theta=tan\theta$
Since sec is equal to 1 over cos, multiply 1 over cos by sin over 1...

$\frac{1}{cos\theta}*\frac{sin\theta}{1}=tan\theta$

$\frac{sin\theta}{cos\theta}=tan\theta$

Since we know that sin over cos is equal to tan...

$tan\theta=tan\theta$

$(sec\theta+tan\theta)(sec\theta-tan\theta)=1$

Start off by foiling...

$sec^2\theta-sec\theta*tan\theta+sec\theta*tan\theta-tan^2\theta=1$

Since there are two places where sec is multiplied by tan, and one is positive and one is negative, they cancel each other out...

$sec^2\theta-tan^2\theta=1$

Since we know that sec minus tan equals 1...

Check out Mr Corn's website HERE for more information and for today's smart board slides.

Posted by kelb at 3:11 PM

Labels: kelseyb, u6#1day1

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