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
Hitman42 [59]
3 years ago
14

Cos(−θ)=√3/3, sinθ<0

Mathematics
1 answer:
Delicious77 [7]3 years ago
7 0

Answer:

\sin\theta=-\frac{\sqrt{6}}{3}


Step-by-step explanation:

The given trigonometric equation is \cos(-\theta)=\frac{\sqrt{3} }{3}.

We can either use the Pythagorean identity or the right angle triangle  to solve for \sin\theta.

According to the Pythagorean identity,

\cos^2\theta+\sin^2\theta=1


Recall that, the cosine function is an even function, therefore

\cos(-\theta)=\cos(\theta)


\Rightarrow \cos(\theta)=\frac{\sqrt{3} }{3}.

We substitute this value in to the above Pythagorean identity to get;


(\frac{\sqrt{3}}{3})^2+\sin^2\theta=1


\Rightarrow \frac{3}{9}+\sin^2\theta=1


\Rightarrow \sin^2\theta=1-\frac{3}{9}


\Rightarrow \sin^2\theta=\frac{6}{9}


\Rightarrow \sin\theta=\pm \sqrt{\frac{6}{9}}


\Rightarrow \sin\theta=\pm \frac{\sqrt{6}}{3}


But we were given that,

\sin\theta\:, so we choose the negative value.

\Rightarrow \sin\theta=-\frac{\sqrt{6}}{3}


The correct answer is B







You might be interested in
Another easy question for Branilist.........
OLEGan [10]

Answer:

-4.5

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
If f(x)=6x^3-4 and g(x)=2x+2, find (f-g)(x)
Lerok [7]

Answer:

https://socratic.org/questions/if-f-x-6x-3-and-g-x-2x-2-find-f-g-x

Step-by-step explanation:

Go to this site. It has the correct answer

8 0
2 years ago
Determine the perimeter of ABCD.
Galina-37 [17]
You add of the sides to get the perimeter.. 9 plus 9 is 18 and 5 plus 5 is 10. 10 plus 18 of 28. The perimeter of ABCD is 28.
I hope this helps.
7 0
3 years ago
last week a worm was 10 millimeters long. This week it is 13 millimeters long. What is the percent of increase of the worm's len
Sladkaya [172]

Answer:

23% increase

Step-by-step explanation:

13 - 10 = 3

3/13 = 0.2307 = 23%

Hope that helped!!! k

7 0
3 years ago
Read 2 more answers
........................​
shtirl [24]

Answer:

Step-by-step explanation:

Figure (1)

x° = 107° [Vertically opposite angles]

Since, vertical angles are equal in measure.

Figure (2)

x + 71° = 90° [Given, complementary angles]

x = 90° - 71°

x = 19°

Figure (3)

x + 21° = 180° [Given as supplementary angles]

x = 180° - 21°

x = 159°

Figure (4)

x = 129° [Vertical angles]

Figure (5)

x° = 90° [Given]

z° + 34° = 90°

z° = 90° - 34°

z° = 56°

Since, x° + y° + z° = 180° [Linear angles]

90° + y° + 56° = 180°

y° + 146° = 180°

y° = 180° - 146°

y° = 34°

7 0
2 years ago
Other questions:
  • A rectangular piece of wood has a perimeter of 18 meters. If we multiply both its length and its width by 4, what will be the pe
    12·2 answers
  • What's the value below??
    14·1 answer
  • On average, the moon is 384,400 kilometers from the Earth . How is this distance written in scientific notation?
    8·1 answer
  • What is 2 1/6 divided by 3 +5 1/2
    15·1 answer
  • What is the mixed number of 45/40
    10·1 answer
  • PLEASE HELP!!<br> In triangle ABC, B= 120 degrees, a=10, c=18, find C
    15·2 answers
  • Please help!! Which two equations are the equations of vertical asymptotes of the function y = 5∕3 tan(3∕4x)?
    7·2 answers
  • Find the next three terms in each sequence. Then write an equation for the nth term of the
    14·1 answer
  • Benny spent 27 minutes talking on the phone on Wednesday. On Thursday, Benny's phone time was 9/10 of Wednesday's time. On Frida
    5·2 answers
  • Help with Math Please... need in 5 min or less.
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!