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
+<br> 3. -5y- 10=-60<br> Solve the equation for -5y- 10=-60
In-s [12.5K]

Answer:

y=10

Step-by-step explanation:

you first add 10 to both sides

the bring down the -5y

thr divide it -50 with -5

6 0
3 years ago
Help please!
Mamont248 [21]

Answer:  see proof below

<u>Step-by-step explanation:</u>

Use the Sum & Difference Identity: cos (A + B) = cos A · cos B - sin A · sin B

Recall the following from Unit Circle: cos (π/2) = 0, sin (π/2) = 1

                                                              cos (π) = -1,   sin (π) = 0    

Use the Quotient Identity:   \tan A=\dfrac{\sin A}{\cos A}

<u>Proof LHS → RHS:</u>

\text{LHS:}\qquad \qquad \dfrac{\cos \bigg(\dfrac{\pi}{2}+x\bigg)}{\cos \bigg(\pi +x\bigg)}

\text{Sum Difference:}\qquad \dfrac{\cos \dfrac{\pi}{2}\cdot \cos x-\sin \dfrac{\pi}{2}\cdot \sin x}{\cos \pi \cdot \cos x-\sin \pi \cdot \sin x}

\text{Unit Circle:}\qquad \qquad \dfrac{0\cdot \cos x-1\cdot \sin x}{-1\cdot \cos x-0\cdot \sin x}

                            =\dfrac{-\sin x}{-\cos x}

Quotient:                 tan x

LHS = RHS \checkmark

7 0
3 years ago
Read 2 more answers
What is an equation of the line that passes through the points (-8,-6) and<br> (3, – 6)?
Maksim231197 [3]

Answer:

y=-6

Step-by-step explanation:

The y value isn't changing when the x value does. This means there is no rate of change or gradient. So in y=mx+c m=0 so we get y=c, c is always -6.

6 0
3 years ago
What financial product am I? I am a type of credit card that requires cardholders to make a security deposit equal to the credit
navik [9.2K]

Answer: secured credit card

Step-by-step explanation:

7 0
2 years ago
A car costing $24,000 is subject to a sales tax of 8%. If Bindu made a $10,000 down payment on his car, what is the tot amount s
Serggg [28]

Answer:

$15,920

Step-by-step explanation:

4 0
11 months ago
Other questions:
  • A cylinder has a volume of 371.776 cubic centimeters. The diameter of the cylinder is 8 cm. What is the height of the cylinder?
    14·1 answer
  • Tom had 50 baseball cards . he kept 10 for himself and shared the rest equally among his 8 friends . how many baseball cards did
    15·1 answer
  • Consider 7x10 power of 3.Write a pattern to find the value of the expression.
    6·1 answer
  • Which of these do you prove with a geometric proof? Select one of the options below as your answer:. . A.. experiments. B.. opin
    14·2 answers
  • What is the answer to 227-198
    5·2 answers
  • Two sides of a triangle have measures 3 ft and 6 ft. Also, these sides form a vertex whose angle measures 60 degrees. Calculate
    15·1 answer
  • Help plzzzzzzzzzzzzzzzzzzzzzzz :(
    9·2 answers
  • What is 1/2 x (8x4+6) + 11<br>pls help
    15·1 answer
  • Cuáles son las partes de un término algebraico
    6·1 answer
  • Someone please help me on both the questions!!!
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!