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Pearson Algebra 1 Common Core, 2011
PA
Pearson Algebra 1 Common Core, 2011 View details
6. Trigonometric Ratios
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Exercise 47 Page 651

Practice makes perfect
a

We can simplify the given expression using the definition of the cosine ratio and the tangent ratio. Let's start by recalling these ratios.

cos(θ) Adjacent leg/Hypotenuse Adj/Hyp
tan(θ) Opposite leg/Adjacent leg Opp/Adj
Now, we will use these ratios to simplify the given product. Let's do it!

cos A * tan A
SubstituteII

cos A= Adj/Hyp, tan A= Opp/Adj

( Adj/Hyp ) * ( Opp/Adj )
MultFrac

Multiply fractions

Adj* Opp/Hyp * Adj
CancelCommonFac

Cancel out common factors

Adj * Opp/Hyp * Adj
SimpQuot

Simplify quotient

Opp/Hyp

Notice that the ratio that we found corresponds to the definition of the sine ratio. Opposite leg/Hypotenuse ⇔ sin A

b

We will use the definition of the sine ratio and the tangent ratio to simplify the given expression.

sin(θ) Opposite leg/Hypotenuse Opp/Hyp
tan(θ) Opposite leg/Adjacent leg Opp/Adj
Let's do it!

sin A ÷ tan A
SubstituteII

sin A= Opp/Hyp, tan A= Opp/Adj

( Opp/Hyp ) ÷ ( Opp/Adj )
DivFracByFracDiv

a/b÷c/d=a/b*d/c

(Opp/Hyp) * (Adj/Opp)
MultFrac

Multiply fractions

Opp* Adj/Hyp * Opp
CancelCommonFac

Cancel out common factors

Opp * Adj/Hyp * Opp
SimpQuot

Simplify quotient

Adj/Hyp

Notice that the ratio that we found corresponds to the definition of the cosine ratio. Adjacent leg/Hypotenuse ⇔ cos A

c

One more time, we will use the definition of the sine ratio and the cosine ratio to simplify the given expression.

sin(θ) Opposite leg/Hypotenuse Opp/Hyp
cos(θ) Adjacent leg/Hypotenuse Adj/Hyp
Let's do it!

sin A ÷ cos A
SubstituteII

sin A= Opp/Hyp, cos A= Adj/Hyp

( Opp/Hyp ) ÷ ( Adj/Hyp )
DivFracByFracDiv

a/b÷c/d=a/b*d/c

(Opp/Hyp) * (Hyp/Adj)
MultFrac

Multiply fractions

Opp* Hyp/Hyp * Adj
CancelCommonFac

Cancel out common factors

Opp * Hyp/Hyp * Adj
SimpQuot

Simplify quotient

Opp/Adj

Notice that the ratio that we found corresponds to the definition of the tangent ratio. Opposite leg/Adjacent leg ⇔ tan A

Subchapter links expand_more
arrow_right Lesson Check p.649
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arrow_right Practice and Problem-Solving Exercises p.649-651
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Practice and Problem-Solving Exercises 17 (Page 649)
Practice and Problem-Solving Exercises 18 (Page 649)
Practice and Problem-Solving Exercises 19 (Page 649)
Practice and Problem-Solving Exercises 20 (Page 649)
Practice and Problem-Solving Exercises 21 (Page 649)
Practice and Problem-Solving Exercises 22 (Page 649)
Practice and Problem-Solving Exercises 23 (Page 649)
Practice and Problem-Solving Exercises 24 (Page 649)
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Practice and Problem-Solving Exercises 36 (Page 650)
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Practice and Problem-Solving Exercises 38 (Page 650)
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Practice and Problem-Solving Exercises 47 (Page 651)
arrow_right Standardized Test Prep p.651
Standardized Test Prep 48 (Page 651)
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Standardized Test Prep 50 (Page 651)
Standardized Test Prep 51 (Page 651)
arrow_right Mixed Review p.651
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Mixed Review 58 (Page 651)
Mixed Review 59 (Page 651)
Mixed Review 60 (Page 651)
Mixed Review 61 (Page 651)