body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Pearson Algebra 2 Common Core, 2011

PA

Pearson Algebra 2 Common Core, 2011 View details

2. Solving Trigonometric Equations Using Inverses

Continue to next subchapter

Exercise 73 Page 918

Recall the Trigonometric Identities. Start by using the Reciprocal Identities $sec θ = \frac{1}{c o s θ}$ and $csc θ = \frac{1}{s i n θ} .$

$cot θ$

Practice makes perfect

At first, let's recall two of the Reciprocal Identities.

sec θ = \frac{1}{cos θ} and csc θ = \frac{1}{sin θ}

With these identities, we can substitute

\frac{1}{c o s θ}

for

sec θ

and

\frac{1}{s i n θ}

for

csc θ

in our expression.

cos^{2} θ sec θ csc θ

$sec θ = \frac{1}{c o s θ}$ , $csc θ = \frac{1}{s i n θ}$

cos^{2} θ \cdot \frac{1}{c o s θ} \cdot \frac{1}{s i n θ}

Multiply fractions

cos^{2} θ \cdot \frac{1}{cos θ sin θ}

MoveLeftFacToNumOne

$a \cdot \frac{1}{b} = \frac{a}{b}$

\frac{cos ^{2} θ}{cos θ sin θ}

$\frac{a}{b} = \frac{a / cos θ}{b / cos θ}$

\frac{cos θ}{sin θ}

Now we will use the Cotangent Identity.

cot θ = \frac{cos θ}{sin θ}

With this identity, we can substitute

cot θ

for

\frac{c o s θ}{s i n θ}

in our expression.

\frac{cos θ}{sin θ}

$\frac{cos θ}{sin θ} = c o t θ$

c o t θ

We have simplified the given expression.

cos^{2} θ sec θ csc θ = cot θ

Subchapter links

Lesson Check p.915

Practice and Problem-Solving Exercises p.916-918

Standardized Test Prep p.918

Mixed Review p.918