Considering only the values of [tex]\beta[/tex] for which [tex]\sin \beta \tan \beta \sec \beta \cot \beta[/tex] is defined, which of the following expressions is equivalent to [tex]\sin \beta \tan \beta \sec \beta \cot \beta[/tex]?

a. [tex]\sec \beta \cot \beta[/tex]
b. [tex]\tan \beta[/tex]
c. [tex]\cot \beta \tan \beta[/tex]
d. [tex]\tan \beta \csc \beta \sec \beta[/tex]

Answers

Answer 1

[tex]\large\boxed{Answer:}[/tex]

We will use trigonometric identities to solve this. I will use θ (theta) for the angle.

First of all, we know that cotθ = 1/tanθ. This is a trigonometric identity.

We can replace cotθ in the expression with 1/tanθ.

[tex]sin\theta tan\theta sec\theta \frac{1}{tan\theta}[/tex]

Simplify: 1/tanθ * tanθ = tanθ/tanθ = 1

So now, we have:

[tex]sin\theta sec\theta[/tex]

Next, we also know that secθ = 1/cosθ. This is another trigonometric identity.

We can replace secθ with 1/cosθ in our expression.

[tex]sin\theta \frac{1}{cos\theta}[/tex]

Simplify:

[tex]\frac{sin\theta}{cos\theta}[/tex]

Our third trigonometric identity that we will use is tanθ = sinθ/cosθ.

We can replace sinθ/cosθ with tanθ.

Now we have as our final answer:

[tex]\large\boxed{b.\ tan\theta}[/tex]

Hope this helps!

Answer 2

Answer:

[tex] \huge \boxed{ \boxed{ \red{b) \tan( \beta ) }}}[/tex]

Step-by-step explanation:

to understand thisyou need to know about:trigonometryPEMDASgiven:[tex]\sin \beta \tan \beta \sec \beta \cot \beta[/tex]tips and formulas:[tex] \tan( \theta) = \dfrac{ \sin( \theta) }{ \cos( \theta) } [/tex][tex] \cot( \theta) = \dfrac{ \cos( \theta) }{ \sin( \theta) } [/tex][tex] \sec( \theta) = \dfrac{1}{ \cos( \theta) } [/tex]

let's solve:[tex] \sf rewrite \: \tan( \beta ) \: as \: \dfrac{ \sin( \beta ) }{ \cos( \beta ) } : \\\sin (\beta ) \cdot\frac{ \sin( \beta ) }{ \cos( \beta ) } \cdot \sec (\beta ) \cdot\cot (\beta)[/tex][tex] \sf rewrite \: \sec( \beta ) \: as \: \dfrac{1 }{ \cos( \beta ) } : \\\sin (\beta) \cdot\frac{ \sin( \beta ) }{ \cos( \beta ) } \cdot \frac{1}{ \cos( \beta ) } \cdot\cot (\beta)[/tex][tex] \sf rewrite \: \cot( \beta ) \: as \: \dfrac{ \cos( \beta ) }{ \sin( \beta ) } : \\\sin (\beta) \cdot\frac{ \sin( \beta ) }{ \cos( \beta ) } \cdot \frac{1}{ \cos( \beta ) } \cdot \: \dfrac{ \cos( \beta ) }{ \sin( \beta ) }[/tex][tex] \sf \: cancel \: sin : \\\sin (\beta) \cdot\frac{ \cancel{\sin( \beta ) }}{ \cos( \beta ) } \cdot \frac{1}{ \cos( \beta ) } \cdot \: \dfrac{ \cos( \beta ) }{ \cancel{\sin( \beta ) }} \\ \sin (\beta) \cdot\frac{ 1 }{ \cos( \beta ) } \cdot \frac{1}{ \cos( \beta ) } \cdot \: \cos( \beta ) \\ [/tex][tex] \sf cancel \: cos : \\ \sin (\beta) \cdot\frac{ 1}{ \cos( \beta ) } \cdot \frac{1}{ \cancel{ \cos( \beta )} } \cdot \: \cancel{ \cos( \beta ) } \\ \\ \sin( \beta ) \: \cdot \: \dfrac{ 1 }{ \cos( \beta ) } [/tex][tex] \sf \: simplify \: multipication : \\ \dfrac{ \sin( \beta ) }{ \cos( \beta ) } [/tex][tex] \sf use \: \frac{ \sin( \beta ) }{ \cos( \beta ) } = \tan( \beta ) \: identity : \\ \therefore \: \tan( \beta ) [/tex]


Related Questions

Olivia has 1/2 pound of raisins. She plans to eat them for snacks over the next 6 days. If she eats the same amount each day, What fraction of a pound of raisins will she eat each day

Answers

Answer :

1/12

Step by step :

Pounds of raisins : 1/2 = 0.5

Number of days : 6

Pounds of raisins she will eat every day :

0.5 ÷ 6 = 0.83333... = 1/12

help 10 points to solve please

Answers

Answer:

A, B, & C are true.

Hope this helps & have a great rest of your day!

Answer:I believe the answer is A,B,C

Step-by-step explanation:

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Answers

Improper Fraction =75/14
Mixed Number=5 5/14

HELP! WILL GIVE BRANLIEST! + EXTRA POINTS!

Answers

Answer:

707 bags of sand

Step-by-step explanation:

To find the area all you have to do is add 40+5+5=50 then you split that in half to get the radius. The you use the area formula to get the entire shape and the get the radius of the smaller circle. Then, you subtract the small circle from the big circle to get the amount of sand needed. When you do that you should get 706.86 but since you need a whole number you would round up to 707

PLEASE HELP‼️‼️
A
B
C
D

Answers

Answer:

C i think

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

use the side splitter theorem

6/12 = x/18 (replacing AQ with x)

12x = 108 (cross multiply)

x = 9

Plz help with this one I have ten minutes to turn it in! Will give u points! And mark u BRAINLY

Answers

i think it’s -3,0,0 but i’m not 100% sure

Step-by-step explanation:

[tex]f(\pi) = - 3 \\ f( \frac{\pi}{2} ) = 0 \\ f( - \frac{3\pi}{2} ) = 0[/tex]

Find the slope of the line that passes through the two points. (-3, -4), (6, 8)

Answers

Answer:

Step-by-step explanation:

let (x1 , y1) = ( - 3, - 4) and (x2 , y2) = ( 6 , 8)

Slope (m)

= y2 - y1 / x2 - x1

= 8 + 4 / 6 + 3

= 12 / 9

= 4/3

Factorise
1) 9a^2 - 6a​

Answers

Answer:

9a^2 - 6a

taking common

3a(3a-2)

HELP PLEASE PLEASE I WILL GIVE BRAINLIEST

Answers

In the top the "f(x)" equals 9, now they are asking you to add onto the 9 by 1 causing it to be 10. If you did the first few you would have noticed that it takes 9 in order to get to 5 from -4.

here are the answers btw:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

it's b.

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Answer:

Th answer to the first question is 18+6=24 the answer to the second question is 9 weeks

Please mark me brainliest!

Suppose that F(x) = x2 and G(X) = 3x2 + 8. Which statement best compares
the graph of G(x) with the graph of Fx)?

Answers

Answer:

the answer is B

Step-by-step explanation:

see the image!

Give Brillianst please!!!!!

Answer:

It’s actually d

Step-by-step explanation:

What is the explicit rule for the arithmetic sequence? 20.5, 16, 11.5, 7, 2.5, ...

Answers

Answer:

To determine the explicit rule for the arithmetic sequence of 20.5, 16, 11.5, 7, 2.5, ..., the following logical reasoning must be performed:

20.5 - 16 = 4.5

16 - 11.5 = 4.5

11.5 - 7 = 4.5

7 - 2.5 = 4.5

Thus, the explicit rule of the arithmetic sequence is that the numbers are gradually subtracted by 4.5, with which the next number of said sequence would be -2.

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Answers

Answer:3/5

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[tex]0=-x2+2x+8[/tex]

Answers

Answer:

x = 4

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Step-by-step explanation:

i need help with this pls.

Answers

Answer:

The answer is D

Step-by-step explanation:

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please help 7m - 10 - 4m + 3

Answers

Step-by-step explanation:

7m - 10 - 4m + 3

3m-7

Hope it helps

7m-10-4m+3
=7m-4m-10+3
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John multiplies 85 by 1.35. Which number might John be trying to find?
A. 135% of 85
B. 35% of 85
C. 13.5% of 85
D. 1.35% of 85

Answers

Answer:

A. 135% of 85

Step-by-step explanation:

When you find the percent of something, you multiply it by 100, so 1.35 ÷ 100 is 135

work out the value of angle x 24 degrees​

Answers

Answer:

180=2x+ 24( angles opposite to equal sides)

156/2=x

x=78

Step-by-step explanation:

The value of x from the triangle is given by the equation x = 78°

What Is an Isosceles Triangle?

A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle

The three types of Isosceles Triangles are :

Isosceles acute triangle

Isosceles right triangle

Isosceles obtuse triangle

Given data ,

Let the triangle be represented as ABC

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It is an isosceles triangle with ∠B = ∠C

So , the measures of the two angles are the same

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Substituting the values in the equation , we get

x + x + 24° = 180°

On simplifying the equation , we get

2x = 156°

Divide by 2 on both sides of the equation , we get

x = 78°

Hence , the measure of x = 78°

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How many minutes is 65% of 3 hours? ____ just write the number part of the answer.

Answers

Answer:

117

Step-by-step explanation:

There are 60 minutes in each hour, and to find how many minutes there are in 3 hours you would have to multiply 3 x 60.

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65 x 180 divided by 100 is 117.

Paul has some money in his wallet, all in $1 bills. He buys a hat and has $6 left, as shown in
the model below.
How much did Paul pay for the hat?
Enter your answer in the box.

Answers

Answer:

we need to see the model

Step-by-step explanation:

model please

When a certain kind of bacterium takes a step, it moves 3 x 10^-7 meters. When
Joe takes a step, he moves 0.75 meters. How many times larger is Joe's step
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Joe's step is[ ] x 10^[ ]
times larger than the bacterium's step

Answers

Answer:

Step-by-step explanation:

0.75/(3*10^(-7)) = 0.25*10^7 = 2.5*10^6

Find n(E), given that n(C×E)=18 and C={4,5,6}

Answers

Answer:

ncx(2.718282)=18;c=456

ncx(2.718282)=18;c=456

f(x)=3x(x^2+4x-5) evaluate f(-2)​

Answers

Answer:

f(-2) = 54

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

f(x) = 3x(x² + 4x - 5)

f(-2) is x = -2

Step 2: Evaluate

Substitute in x  [Function]:                                                                             f(-2) = 3(-2)[(-2)² + 4(-2) - 5][Brackets] Evaluate exponents:                                                                     f(-2) = 3(-2)[4 + 4(-2) - 5][Brackets] Multiply:                                                                                         f(-2) = 3(-2)[4 - 8 - 5][Brackets] Subtract:                                                                                        f(-2) = 3(-2)[-4 - 5][Brackets] Subtract:                                                                                        f(-2) = 3(-2)(-9)Multiply:                                                                                                           f(-2) = -6(-9)Multiply:                                                                                                           f(-2) = 54

WILL MARK BRAINLELIST HELPPPP ME

Answers

Answer:

17

Step-by-step explanation:

180 - 5 - 5 = 170 : 2 = 85 : 5 = 17

PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!

Answers

Answer:

One solution

Step-by-step explanation:

Basicly its just seeing if x can be anything, nothing or one thing so x · 0 = 0 has infinite answers, 4x + 6 = 11 has one solution, and 0x = 5 has no solution

Simplify the expression:
2n + 10(9 + 4n)

Answers

Answer:

42n+90

Step-by-step explanation:

Answer: 42n+90
Explaination:

2
n
+
10
(
9
+
4
n
)
Distribute:
=
2
n
+
(
10
)
(
9
)
+
(
10
)
(
4
n
)
=
2
n
+
90
+
40
n
Combine Like Terms:
=
2
n
+
90
+
40
n
=
(
2
n
+
40
n
)
+
(
90
)
=
42
n
+
90

Which of the lines below has a negative slope?
A
B
6
-5
15
6
10
5
D
5
5

Answers

Well, negative slope has the word negative in it right? So, it will be the negative number. Answer: -5 (negative 5)

PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((

Answers

I'm only sure about the second one

Answer:

Yes

Step-by-step explanation:

(2, 1) is a solution to the given system of linear equations.

x + 16y = 2 + 16*1 = 2 + 16 = 18

2x + 11y = 2*2 + 11*1 = 4 + 11 = 15

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