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
german
2 years ago
5

Evaluate each of the following expressions by using special right triangles and the unit circle (give exact values),

Mathematics
1 answer:
levacccp [35]2 years ago
3 0

Using equivalent and fundamenta. angles, we find that:

a) \sin{\left(\frac{4\pi}{3}\right)} = \frac{\sqrt{3}}{2}

b) \cos{\left(\frac{11\pi}{3}\right)} = \frac{1}{2}

c) \sin{\left(-\frac{5\pi}{3}\right)} = -\frac{1}{2}

d) \cos{\left(-\frac{2\pi}{3}\right)} = -\frac{1}{2}

Item a:

\frac{4\pi}{3} is an angle in the third quadrant, as \pi < \frac{4\pi}{3} < \frac{3\pi}{2}

It's equivalent in the first quadrant is: \frac{4\pi}{3} - \pi = \frac{\pi}{3}, which is a fundamental angle, which means that it's values of sine, cosine and tangent are known.

Sine in the third quadrant is negative, while in the first is positive, thus:

\sin{\left(\frac{4\pi}{3}\right)} = -\sin{\left(\frac{\pi}{3}\right)} = \frac{\sqrt{3}}{2}

Item b:

\frac{11\pi}{3} = 2\pi + \frac{5\pi}{3}

Thus, it is equivalent to an angle of \frac{5\pi}{3}, which is in the fourth quadrant.

It's equivalent on the first quadrant is:

2\pi - \frac{5\pi}{3} = \frac{\pi}{3}

Cosine in the fourth quadrant is positive, just as in the first, thus:

\cos{\left(\frac{11\pi}{3}\right)} = \cos{\left(\frac{\pi}{3}\right)} = \frac{1}{2}

Item c:

2\pi - \frac{5\pi}{6} = \frac{7\pi}{6}

Which is a angle in the third quadrant.

It's equivalent in the first is:

\frac{7\pi}{6} - \pi = \frac{\pi}{6}

Sine in the third quadrant is negative, while in the first is positive, thus:

\sin{\left(-\frac{5\pi}{6}\right)} = \sin{\left(\frac{7\pi}{6}\right)} = -\sin{\left(\frac{\pi}{6}\right)} = -\frac{1}{2}

Item d:

2\pi - \frac{2\pi}{3} = \frac{4\pi}{3}

Which is in the third quadrant.

Cosine in the third quadrant is negative, while in the first is positive, thus:

\cos{\left(\frac{-2\pi}{3}\right)} = \cos{\left(\frac{4\pi}{3}\right)} = -\cos{\left(\frac{\pi}{3}\right)} = -\frac{1}{2}

A similar problem is given at brainly.com/question/23843479

You might be interested in
.<br> 8.) A can of tennis balls is $4.00 and is 15% off. The sales tax is 6%.<br><br> Help pls
Ostrovityanka [42]

Answer:

$3.64 is the answer I hope it helps

3 0
3 years ago
Read 2 more answers
If anyone knows how to do this
iogann1982 [59]

Answer:

1) 47

2) 4

Step-by-step explanation:

Complimentary = 90 degrees

1) 43 + ? = 90

? = 47

2) 86 + ? = 90

? = 4

8 0
3 years ago
Can u guys PLEASE answer this question ASAP. THIS IS EXTREMELY URGENT
skelet666 [1.2K]

Answer:

14.55 hope this help

Step-by-step explanation:

3 0
3 years ago
15. An irregular pentagon has side lengths of (x + 3), (2x - 4), (4x + 5),
Tcecarenko [31]
I’m my opinion I thick it could be A
7 0
3 years ago
Which division problem is equivalent to 25?
meriva
They all add up to 2.5 maybe u have to simplify?
4 0
3 years ago
Other questions:
  • Can someone please help me with this? (20 points)
    14·2 answers
  • Simplify the complex fraction:<br> (49-x^2)^1/2 + 9x^2(49-x^2)^-1/2 / 49-x^2
    7·1 answer
  • A _________________is a numerical value that describes a population.
    10·2 answers
  • The data represents the daily rainfall​ (in inches) for one month. Construct a frequency distribution beginning with a lower cla
    10·1 answer
  • On November 7, 2013, Twitter began to sell shares of its company and Naomi purchased 20 shares for $26 each. It went up $3.15 ev
    8·1 answer
  • Mike is overdrawn at the bank by $18. His sister has $23 more than him. How much does
    11·2 answers
  • The box plots compare the number of students in Mr. Ishimoto’s classes and in Ms. Castillo’s classes over the last two semesters
    6·2 answers
  • Points if anyone wants them will mark brainlest
    6·1 answer
  • Solve<br> -21 = -9 + 2/3b
    14·1 answer
  • if there are 48 students in a class and 42% of those students have a dog what percent of students have a dog or a cat?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!