Download - Trigo Assignment 5

7/31/2019 Trigo Assignment 5

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Reciprocal Identities

Pythagorean Identities

Co-function Identities

Addition Formulas

sin (a + b) = sin a cos b + cos a sin b

cos (a + b) = cos a cos b sin a sin b


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Subtraction Formulas

sin (a - b) = sin a cos b - cos a sin b

cos (a - b) = cos a cos b + sin a sin b

Double Angle Formulas

sin 2a = 2 sin a cos a

cos 2a = cos 2a sin 2a = 2 cos 2a 1 = 1 2 sin 2a

Even-odd Identities

Sum-to-product Formulas


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Product-to-sum Formulas

12.b.

Take thecosine of to get

Take thecotangent of to get 1.

Take thecosecant of to get 2.

Multiply by 1 to get
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Multiply by 2 to get 1.

x=(1)

Remove the parentheses around the expression1.

x=1

12.c.

12.e.

Squaring an expression is the same as multiplying the expression by itself2 times.

Multiply each term in the first group by each term in the second group using the FOILmethod. FOIL stands for FirstOuterInnerLast, and is a method of multiplying two

binomials. First, multiply the first two terms in each binomial group. Next,multiply the

outer terms in each group, followed by the inner terms. Finally, multiply the last two

terms in each group.

Simplify the FOILexpression by multiplying and combining all like terms.

Squaring an expression is the same as multiplying the expression by itself2 times.
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Multiply each term in the first group by each term in the second group using the FOIL

method. FOIL stands for FirstOuterInnerLast, and is a method of multiplying two

binomials. First, multiply the first two terms in each binomial group. Next,multiply the

outer terms in each group, followed by the inner terms. Finally, multiply the last twoterms in each group.

Simplify the FOILexpression by multiplying and combining all like terms.

Remove the parentheses that are not needed from the expression.

Since and are like terms, add to to get

Since 4cos(x)sin(x) and -4cos(x)sin(x) are like terms, add -4cos(x)sin(x) to

4cos(x)sin(x) to get 0.

Since and are like terms, add to to get
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Replace with 5 using the identity

5=y

Since y is on the right-hand side of theequation, switch the sides so it is on the left-

hand side of the equation.

y=5

12.f.

Invert the trigonometric factorin the denominator.


Take thecosine of50 to get 0.64.

Expand the exponent(2) to theexpression.

Squaring a number is the same as multiplying the number by itself In

this case, 0.64 squared is 0.41.
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Remove the parentheses around the expression0.41.





0.41+(0.59)=y


0.41+0.59=y

Add 0.59 to 0.41 to get 1.

1=y

Since y is on the right-hand side of theequation, switch the sides so it is on the left-hand side of the equation.

y=1
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12.g.

Take thecosine of110 to get -0.34.

Take thecosine of160 to get -0.94.

Multiply-1 by the -0.94 inside the parentheses.

Add 0.94 to -0.34 to get 0.6.

Take thesine of70 to get 0.94.


Add 0.94 to 0.94 to get 1.88.

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Squaring a number is the same as multiplying the number by itself In this

case, 0.6 squared is 0.36.




(0.36)+(3.53)=y

Remove the parentheses that are not needed from the expression.

0.36+3.53=y

Add 3.53 to 0.36 to get 3.89.

3.89=y

Since y is on the right-hand side of theequation, switch the sides so it is on the left-


y=3.89

12.h.
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To add fractions, the denominators must be equal. Thedenominators can be made equal

by finding the least common denominator(LCD). In this case, the LCD is

Next, multiply each fraction by a factorof1 that will create the LCD in each of the

fractions.

Complete the multiplication to produce a denominatorof in each expression.

Combine thenumerators of all expressions that have common denominators.


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Squaring a number is the same as multiplying the number by itself

In this case, 0.259 squared is 0.067.


Take thetangent of75 to get 3.732.





Multiply0.067 by 13.928 to get 0.933.
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Multiply-1 by the 0.933 inside the parentheses.

Subtract 0.933 from 1 to get 0.067.





Divide0.067 by 0.067 to get 1.

1=x
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Since x is on the right-hand side of theequation, switch the sides so it is on the left-


x=1

13.a.

Replace with an equivalentexpression using the fundamental

identities.

Rewrite the expression using the identity.

13.c.

Multiply by each term inside the parentheses.

Remove the parentheses around the expression
http://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equivalenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=identityhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/detail.aspx?=130498http://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equivalenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=identityhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expression


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Replace with an equivalentexpression using the fundamental identities.

Replace with an equivalentexpression using the fundamental

identities.

Remove the common factors that were cancelled out.

Combine all similarvariables in the expression.

To add fractions, the denominators must be equal. The denominators can be made

equal by finding the least common denominator(LCD). In this case, the LCD is

Next, multiply each fraction by a factorof1 that will create the LCD in

each of the fractions.

Complete the multiplication to produce a denominatorof in each

expression.
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Combine the numerators of all expressions that have common denominators.

Replace with 1 using the identity

Replace with an equivalentexpression in the numerator.

Since x is on the right-hand side of the equation, switch the sides so it is on the

left-hand side of the equation.

13.e.

Since 1 does not contain the variable to solve for, move it to the right-hand side

of the equation by subtracting 1 from both sides.

Simplify the right-hand side of the equation.
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16/21

Multiply each term in the equation by -1.

Multiply-x by -1 to get x.

Simplify the right-hand side of the equation by simplifying each term.

Replace with using the identity

Factorout the GCF of from each term in the polynomial.

Factorout the GCF of from

Reduce the expression by canceling out the common factorof from
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17/21

the numeratorand denominator.

Reduce the expression by canceling out the common factorof from

the numeratorand denominator.

13.f.



Remove the extra parentheses around the factors.

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18/21

Rewrite the factorof using the identity which in this case leads to

Reduce the expression by canceling out the common factors.

1=x

Since x is on the right-hand side of theequation, switch the sides so it is on the left-


x=1

13.g.



Multiply each term by a factorof1 that will equate all the denominators. In this

case, all terms need a denominatorof The

expression needs to be multiplied by to make the denominator

The expression needs to be multiplied by

to make the denominator
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19/21

Multiply the expression by a factorof1 to create the least common denominator

(LCD) of


Multiply the expression by a factorof1 to create the least common denominator

(LCD) of


The numerators ofexpressions that have equal denominators can be combined. In

this case, and have the same

denominatorof so the numerators can be combined.

Simplify the numeratorof the expression.
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20/21

Since and are like terms, subtract from to get 0.

13.h.

Convert the to its equivalent.




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21/21

14.a