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bearhunter [10]
3 years ago
5

How do you evaluate sin(13π/12)?

Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
7 0

13pi/12 lies between pi and 2pi, which means sin(13pi/12) < 0

Recall the double angle identity,

sin^2(x) = (1 - cos(2x))/2

If we let x = 13pi/12, then

sin(13pi/12) = - sqrt[(1 - cos(13pi/6))/2]

where we took the negative square root because we expect a negative value.

Now, because cosine has a period of 2pi, we have

cos(13pi/6) = cos(2pi + pi/6) = cos(pi/6) = sqrt[3]/2

Then

sin(13pi/12) = - sqrt[(1 - sqrt[3]/2)/2]

sin(13pi/12) = - sqrt[2 - sqrt[3]]/2

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How many solution does this have and how do you solve it
Vadim26 [7]

Answer:

Infinite solutions

Step-by-step explanation:

To determine the number of solutions a system has, you need its slope. If the slopes are the same, check if the equations are equivalent or not.

To find the slope, rearrange the equation to isolate "y", which makes it slope-intercept form y = mx + b.

"x" and "y" represent points on the line.

"m" represents the slope, which is how steep a line is.

"b" represents the y-intercept (where the graph hits the y-axis).

Isolate "y" in both equations:

x + 3y = 0

3y = -x        Subtract 'x' from both sides

y = -x/3        Divide both sides by 3.

y = -\frac{1}{3}x

The slope is -1/3.

9y = -3x

y = -3x/9        Divide both sides by 9

y = -\frac{3}{9}x        Reduce the fraction to lowest terms

y = -\frac{1}{3}x

The slope is -1/3, but the two equations are the same.

Since the equations are the same, or <u>equivalent</u>, the two lines are always touching. The solution of a system means where two lines intersect, or meet. Therefore, <u>there are infinite solutions</u>.

5 0
3 years ago
Please explain how to do this question ;^;
Elena-2011 [213]
I need to know which question it is though
8 0
3 years ago
n 2000 the population of a small village was 2,400. With an annual growth rate of approximately 1.68%, compounded continuously,
Nitella [24]

Answer:

The population would be 3358

Step-by-step explanation:

Since, exponential growth function if the growth is compound continuously,

A = Pe^{rt}

Where,

P = initial population,

r = growth rate per period,

t = number of periods,

Given,

The population in 2000, P = 2,400,

Growth rate per year = 1.68% = 0.0168,

Number of years from 2000 to 2020, t = 20,

Thus, the population in 2020,

A=2400 e^{0.0168\times 20}

=2400 e^{0.336}

= 3358.4136

\approx 3358

6 0
3 years ago
Mariko needs about 18 wheelbarrows full of stone for her Japanese garden. Her wheelbarrow has vertical sides with the given shap
zlopas [31]

Answer:

I don't know yet haheuehehheejejejej

3 0
3 years ago
Another question what's the formula for an open end of a cylinder??​
Kay [80]

Answer:

Formula for an opened end of a cylinder =

\pi r^2 +2\pi rh\\

Closed at both end =

2\pi r^2 +2\pi r h

Opened at both end =

2\pi rh

Step-by-step explanation:

6 0
2 years ago
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