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
Readme [11.4K]
3 years ago
14

Can anyone please show me how to find sin 18 in fraction form? plzzzzzzz $_$​

Mathematics
1 answer:
Inessa [10]3 years ago
7 0

Answer:

(-1 + √5) / 4

Step-by-step explanation:

18° is 1/5 of 90°. So if we say x = 18:

5x = 90

You probably won't find an identity for sin(5x) in your textbook.  But you will find double angle and triple angle formulas.  So if we split 5x into two terms:

2x + 3x = 90

Rearrange:

2x = 90 − 3x

Take sine of both sides:

sin(2x) = sin(90 − 3x)

Use phase shift identity:

sin(2x) = cos(3x)

Apply double and triple angle formulas:

2 sin x cos x = 4 cos³ x − 3 cos x

Simplify:

0 = 4 cos³ x − 3 cos x − 2 sin x cos x

0 = cos x (4 cos² x − 3 − 2 sin x)

We know cos 18° isn't 0, so we can divide it out:

0 = 4 cos² x − 3 − 2 sin x

Using Pythagorean identity and simplifying:

0 = 4 (1 − sin² x) − 3 − 2 sin x

0 = 4 − 4 sin² x − 3 − 2 sin x

0 = 1 − 4 sin² x − 2 sin x

0 = 4 sin² x + 2 sin x − 1

Solve with quadratic formula (or you can complete the square):

sin x = [ -2 ± √(2² − 4(4)(-1)) ] / 2(4)

sin x = [ -2 ± √(4 + 16) ] / 8

sin x = (-2 ± √20) / 8

sin x = (-2 ± 2√5) / 8

sin x = (-1 ± √5) / 4

18° is in the first quadrant, so we know sin x > 0.  Therefore:

sin x =  (-1 + √5) / 4

You might be interested in
Which set of ordered pairs is a function?
Juliette [100K]

Answer:the answer is {( -5,1),(-3,2),(-1,3),(1,4),(3,5)}

Step-by-step explanation: The x should not repeat

6 0
2 years ago
Over the last three evenings, Ashley received a total of 106 phone calls at the call center. The third evening, she received 2 t
V125BC [204]
Change X and Z. X is first evening
Y is second
Z is third evening

5 0
3 years ago
Given: m∠1 = 140°, find m∠6.
zavuch27 [327]
<h2><em><u>Ans</u></em><em><u>wer</u></em><em><u>:</u></em></h2>

Let m<6 be X

140° + X = 180°

X = 180° - 140°

X =40°

5 0
3 years ago
What is 0.015 x 1.5=
alukav5142 [94]
The answer is 0.0225
7 0
3 years ago
Can you please help me answer this question what's a+3
Inessa [10]

Answer:

a+3

Step-by-step explanation:

You cannot go any further in answering this question.  These two terms are not like terms so they cannot be combined.  Therefore, the answer is just a+3 itself.

7 0
3 years ago
Other questions:
  • A cubic centimeter can be expressed as<br> a.cm3 or cc<br> b. ccm<br> c. ccm3<br> or d.ct
    10·2 answers
  • Find the area of the rectangle. 8 cm 16 cm​
    6·2 answers
  • What is the volume of a hemisphere with a radius of 30.8 cm, rounded to the nearest tenth of a cubic centimeter?
    8·1 answer
  • If there are 80 calories in 2/3 of an apple, How many calories are in 6 apples?
    13·1 answer
  • I WILL MARK BRAINIEST
    15·1 answer
  • Which is the right answer?????
    9·1 answer
  • .....................
    10·1 answer
  • Solve psl brainliest
    13·2 answers
  • The Empire State Building is 1,454 feet tall (if you include the lightning rod). If a piece of gum is dropped from the top, how
    12·1 answer
  • Which conversion requires multiplication?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!