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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

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5 0
3 years ago
Which ordered pair is a solution for 3x + 4y &lt; 12?
Andre45 [30]

Answer:

D, (1,2)

Step-by-step explanation:

It all comes down to substitution. In this case the coefficient of x is 3 and the coefficient of y is 4. The format of these coordinates being (x,y).

1. Plug in your x value (1 in this circumstance) and solve:

3(1) + 4y < 12

3 + 4y < 12

2. Plug in your y value (2 in this circumstance) and solve:

3 + 4(2) < 12

3 + 8 < 12

3. Solve

3 + 8 = 11

11 < 12

5 0
3 years ago
Help asap !! will get branliest.​
kompoz [17]

Answer:

0.8

Step-by-step explanation:

(2 x 10^-4)

= 0.0002

(4x10^3)

= 4000

0.0002 x 4000 = 0.8

7 0
3 years ago
Plzzzzz helps meee I don’t get this
Inessa05 [86]
1 way : 10d + 2d

another way: 5d + 5d + 2d
4 0
3 years ago
Almost done. I need help with this part
valentina_108 [34]

Answer:

\%Percent = 14.3\%

Step-by-step explanation:

Required

15 is what percentage of 105

To do this, simply divide 15 by 105 multiplied by 100%.

So, we have:

\%Percent = \frac{15}{105} * 100\%

\%Percent = \frac{15*100}{105}\%

\%Percent = \frac{1500}{105}\%

\%Percent = 14.3\% --- approximated

8 0
3 years ago
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