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
dimaraw [331]
2 years ago
11

Use trig identities to calculate sin(2x) and cos(2x) based on given information tanx=2 and cosx>0

Mathematics
1 answer:
kifflom [539]2 years ago
4 0

Answer:

Find sin 2x, knowing tan x = -2, and cos x > 0

Ans:

sin

2

x

=

4

5

Explanation:

3 Trig identities to be used:

1

+

tan

2

x

=

1

cos

2

x

(1)

sin

2

x

+

cos

2

x

=

1

(2)

sin

2

x

=

2

sin

x

.

cos

x

(3)

Given tan x = -2. First find cos x and sin x

(1) -->

1

+

4

=

1

cos

2

x

-->

cos

2

x

=

1

5

-->

cos

x

=

±

1

√

5

.

Since cos x > 0, then

cos

x

=

1

√

5

.

(2) -->

sin

2

x

=

1

−

cos

2

x

=

1

−

1

5

=

4

5

-->

sin

x

=

±

2

√

5

.

Since cos x > 0 then

sin

x

=

2

√

5

.

(3) -->

sin

2

x

=

2

sin

x

.

cos

x

=

2

(

1

√

5

)

(

2

√

5

)

=

4

5

Answer link

You might be interested in
I NEED HELP PLEASE, THANKS! :)
NISA [10]

Answer:   \bold{b)\quad \dfrac{2\pi}{3},\dfrac{4\pi}{3},0}

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

Note the following identities: tan² x = sec²x - 1

                                                 \sec x=\dfrac{1}{\cos}

tan² x + sec x = 1

(sec² x -1) + sec x = 1

sec² x + sec x - 2 = 0

(sec x + 2)(sec x - 1) = 0

sec x + 2 = 0     sec x - 1 = 0

sec x = -2          sec x = 1

\dfrac{1}{\cos x}=-2\qquad \dfrac{1}{\cos x}=1\\\\\cos x=-\dfrac{1}{2}\qquad \cos x=1\\\\x=\dfrac{2\pi}{3}, \dfrac{4\pi}{3}\qquad x=0

8 0
3 years ago
Read 2 more answers
Add the two expressions <br> -4.2x+3 and 2.5x-6<br><br><br> please help me with this
dalvyx [7]

-1.7×-6 is the answer. Hope this helps.

6 0
3 years ago
Read 2 more answers
What is 4f - 24 + 4f = -8
Lynna [10]

Answer:

F = 2

Step-by-step explanation:

4f-24+4f=-8

collect like terms

8f-24=-8

move constant to the right

8f=-8+24

calculate

8f=16

divide both sides by 8

Answer F = 2

3 0
3 years ago
A company was able to increase its staff from 127 employees to 204
alekssr [168]
The percentage increase in staff was 60.6%.
8 0
3 years ago
Match the following rational expressions to their rewritten forms.
Nookie1986 [14]

Answer:

Answer image is attached.

Step-by-step explanation:

Given rational expressions:

1.\ \dfrac{x^2+x+4}{x-2}\\2.\ \dfrac{x^2-x+4}{x-2}\\3.\ \dfrac{x^2-4x+10}{x-2}\\4.\ \dfrac{x^2-5x+16}{x-2}

And the rewritten forms:

(x-2)+\dfrac{6}{x-2}\\(x+3)+\dfrac{10}{x-2}\\(x+1)+\dfrac{6}{x-2}\\(x-3)+\dfrac{10}{x-2}

We have to match the rewritten terms with the given expressions.

Let us consider the rewritten terms and let us solve them one by one by taking LCM.

(x-2)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x-2)^{2}+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+4+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+10}{x-2}

So, correct option is 3.

(x+3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x+3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{(x^2+3x-2x-6)+10}{x-2}\\\Rightarrow \dfrac{x^2+x+4}{x-2}

So, correct option is 1.

(x+1)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x+1)(x-2)+6}{x-2}\\\Rightarrow \dfrac{x^{2} +x-2x-2+6}{x-2}\\\Rightarrow \dfrac{x^{2} -x+4}{x-2}

So, correct option is 2.

(x-3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x-3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{x^2-3x-2x+6+10}{x-2}\\\Rightarrow \dfrac{x^2-5x+16}{x-2}

So, correct option is 4.

The answer is also attached in the answer area.

7 0
2 years ago
Other questions:
  • Is the following sentence a statement or not a statement?
    14·2 answers
  • Which graph is an example of a function whose parent graph is of the form y = √x?
    11·2 answers
  • Aidan has 6 (different) bulls and 10 (different) horses living at his animal sanctuary. He needs to place them in a line of 16 p
    8·1 answer
  • Can someone answer this plz im giving brainliest
    12·2 answers
  • Answer all or none! Ty!​
    11·1 answer
  • Please answer the picture
    6·1 answer
  • Point D is on line segment \overline{CE}
    6·1 answer
  • This is due in 10 minutes please help me
    9·1 answer
  • Help fast I'm dum
    7·2 answers
  • The median price, P, of a home rose from 80$ thousand in 1980 to 240$ thousand in 2000. Let t be the number of years since 1980.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!