1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alex73 [517]
3 years ago
7

I'm confused on how to do this. Please explain step by step. If you respond with just the answer I WILL report you. I would like

an explanation. Thank you

Mathematics
1 answer:
Tcecarenko [31]3 years ago
4 0

Answer:

Exact Form:

√2−1

Decimal Form:

0.41421356

…

Step-by-step explanation:

Since  9π/8  is not an angle where the values of the six trigonometric functions are known, try using half-angle identities.

9π/8  is not an exact angle

First, rewrite the angle as the product of  1/2  and an angle where the values of the six trigonometric functions are known. In this case,  9π/8  can be rewritten as

(1/2)*  9π/8 tan ((1/2)*  9π/8)

Use the half-angle identity for tangent to simplify the expression. The formula states that  

tan (0/2)=sin(0)/1+cos(0) sin(9π/4)/1+cos(9π/4)

Simplify

Remove full rotations of  2π  until the angle is between  0  and  2π.

sin(π/4)/1+cos(9π/4)

The exact value of sin(π/4) is √2/2

√2/2/1+cos(9π/4)

Simplify the Denominator

Remove full rotations of  2π  until the angle is between  0  and  2π.√2/2/1+cos(π4)

The exact value of cos(π/4)   is  √2/2.√2/2/1+√2/2

To write  1/1  as a fraction with a common denominator, multiply by  2/2  .√2/2/1/1⋅2/2+√2/2

Write each expression with a common denominator of  2, by multiplying each by an appropriate factor of  1.

Combine.

√2/2/1⋅2/1⋅2+√2/2

Multiply 2 by 1

√2/2/1⋅2/2+√2/2

Combine the numerators over the common denominator.

√2/2/1⋅2+√2/2

Multiply 2 by 1

√2/2/2+√2/2

Multiply the numerator by the reciprocal of the denominator

√2/2  ⋅  2/2+√2

Cancel the common factor of  2  .

Factor out the greatest common factor  2

√2/2⋅1  ⋅  2⋅1/2+√2

Cancel the common factor

√2/2⋅1  ⋅  2⋅1/2+√2

Rewrite the expression.

√2/1  ⋅  1/2+√2

Simplify

Multiply  √2/1  and  1/2+√2

√2/2+√2

Multiply  √2/2+√2  by  2−√2/2−√2

Combine

√2(2−√2)/(2+√2)(2−√2)

Expand the denominator using the FOIL method.

√2(2−√2)/4−2√2+√2⋅2−√2^2

Simplify

√2(2−√2)/2

Apply the distributive property

√2⋅2+√2(−√2)/2

Move  2  to the left of the expression  √2⋅2.

2⋅√2+√2(−√2)/2

Simplify  

√2(−√2)  .

Raise  √2  to the power of  1  .

2⋅√2−(√2^1√2)/2

Raise  √2  to the power of  1  .

2⋅√2−(√2^1√2^1)/2

Use the power rule  a^m  a^n=a^m+n  to combine exponents.

2⋅√2−√2^1+1/2

Add  1  and  1  .

2⋅√2−√2^2/2

Simplify each term.

Multiply  2  by  √2  .

2√2−√2^2/2

Rewrite  √2^2  as  2  .

2√2−1⋅2/2

Multiply  −1  by  2.

2√2−2/2

Reduce the expression by cancelling the common factors.

Factor  2  out of  2√2.

2(√2)−2/2

Factor  2  out of  −2.

2(√2)+2⋅−1/2

Factor  2  out of  

2(√2)+2(−1)2(√2−1)/2

Cancel the common factors.

Factor  2  out of  2  .

2(√2−1)/2(1)

Cancel the common factor.

2(√2−1)/2⋅1

Rewrite the expression.

√2−1/1

Divide  √2−1  by  1  .

√2−1

The result can be shown in multiple forms.

Exact Form:

√2−1

Decimal Form:

0.41421356…

Hope it help. Good luck.

You might be interested in
What is the value of X? Enter answer as a decimal...
lozanna [386]

Answer:

37.89051724=x

Step-by-step explanation:

We can use similar triangles and proportions to solve.  Put the same side of the small triangle over the large triangle.

MA         MB

------- = ----------

MN         MP

80.5 -35         x

------------- = ----------

70.5               96.6 -x

Simplifying

45.5             x

------------- = ----------

70.5               96.6 -x

Using cross products

45.5 (96.6-x) = 70.5x

Distribute

4395.3 - 45.5 x = 70.5x

Add 45.5x to each side

4395.3 - 45.5 x+45.5x = 70.5x+45.5x

4395.3 = 116x

Divide each side by 116

4395.3/116 = 116x/116

37.89051724=x

6 0
3 years ago
Frank is planting a flower garden. He plants 2 lilies for every 3 rose bushes. If Frank plants 12​ lilies, how many rose bushes
Alja [10]

Answer:

17 rose  bushes

Step-by-step explanation:

Add all of them together  to find the answer. HOPE this helps:> please mark brainliest

7 0
3 years ago
Read 2 more answers
Help me out 7th grade math
Dmitrij [34]

Answer:

x=9

Step-by-step explanation:

5+18=23

50-23=27

27/3=9

5 0
3 years ago
Select the correct answer from the drop-down menu.
Svetllana [295]
X^3-2x^2-5x+6
From the shape, you can immediately tell it’s one of the x^3 functions. Then I just put both in my calculator and looked for which one matched
8 0
2 years ago
Identify the question that is NOT statistical.
avanturin [10]
<span>A)What is the maximum number of swimmers allowed on a swim team?</span>
6 0
3 years ago
Other questions:
  • Explain how to solve 643 = 4x160 +n
    15·2 answers
  • Find the coordinates of the midpoint of a segment with the given end points V(-2,5) Z(3,-17)
    15·2 answers
  • Use the formula for finding the surface area of a rectangular prism.
    9·1 answer
  • Simplify each expression. Write answers with only positive exponents. Assume that all variables represent positive real numbers.
    15·1 answer
  • What is the value of x?
    5·1 answer
  • If the prism has 3 layers, what would the volume of the
    10·1 answer
  • Which of the following represents a reflection of (-3, 4) across the y-axis?
    13·1 answer
  • What is 40 tens 4 tenths 80 hundredths and 102 thousandths
    11·2 answers
  • Please answer this with full explanation.
    15·2 answers
  • Time magazine reported the result of a telephone poll of 800 adult Americans. The question posed of the Americans who were surve
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!