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2 years ago

If sin(32)=x , then sin(4) cos(4) cos(8) cos(16)=..............

1 answer:

6 0

If sin 32 is equal to x, then sin 4 · cos 4 · cos 8 · cos 16 is equal to x/8 by using double angle trigonometric functions.

<h3>How to simplify an expression by trigonometric expressions</h3>

Trigonometric expressions are formulas that utilize trigonometric functions. Trigonometric functions are a kind of trascendental functions, that is, functions that cannot be described in algebraic terms.

In this question we must simplify a given expression by using the following trigonometric formula:

sin 2x = 2 · cos x · cos x (1)

Now we proceed to expand the expression given:

x = sin 32

x = 2 · sin 16 · cos 16

x = 4 · sin 8 · cos 8 · cos 16

x = 8 · sin 4 · cos 4 · cos 8 · cos 16

Thus,

sin 4 · cos 4 · cos 8 · cos 16 = x/8

If sin 32 is equal to x, then sin 4 · cos 4 · cos 8 · cos 16 is equal to x/8 by using double angle trigonometric functions. $\blacksquare$

To learn more on trigonometric functions, we kindly invite to check this verified question: brainly.com/question/6904750

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How do I Simplify 4a – 7b + 2ab – a + b (I need step by step cause I'm trying to learn this)

Alex

Step-by-step explanation:

Ok. First of all, we need to follow the order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. We don't have any parentheses, exponents, or division to resolve, so you can skip those. So now you have: Multiplication, Addition, and Subtraction. We have multiplication in each term, but each term is fully simplified, so we have Addition and Subtraction left.

With that out of the way, let's go ahead and rearrange this equation so it is easier to solve. (Note: we can only rearrange terms that are positive because subtraction is not commutative. But we can turn negative terms into "positive" terms by the method shown below.)

4a - 7b + 2ab - a + b

4a + (-7b) + 2ab + (-a) + b (Now the terms are all positive, so we can rearrange them, but they still have the same value.)

4a + (-a) + 2ab + (-7b) + b

3a + 2ab + 7b

And there we go. Our answer is fully simplified. If you can understand this, you'll be able to simplify without isolating and rearranging the terms each time.

Hopefully this was helpful and not confusing.

4 0

3 years ago

Lin rode her bike 2 miles in 8 minutes. She rode at a constant speed. Complete the table to show the time it took her to travel

pantera1 [17]

Answer:

The answer is 56

Step-by-step explanation:

I'm smart and you are dumb

8 0

3 years ago

In 2003 a town’s population was 1431. By 2007 the population had grown to 2134. Assume the population is changing linearly.How m

sergiy2304 [10]

We will have the following:

First, we will have that the population change by:

$\Delta P=2134-1431\Rightarrow\Delta P=703$

So, the population changed by 703 people.

It took the follwoing number of years to change from 1431 to 2134:

$\Delta y=2007-2003\Rightarrow\Delta y=4$

So, it took 4 years to changes from 1431 to 2134.

$m=\frac{2134-1431}{2007-2003}\Rightarrow m=175.75$

The average population growth per year is of 175.75 people per year.

The population in 2000 would have been:

$P_{2000}=\frac{2000\cdot1431}{2003}\Rightarrow P_{2000}=1428.856715\ldots$

$\Rightarrow P_{2000}\approx1429$

So, the population in 2000 would have been approximately 1429 people.

We will have that the equation for the population would be:

$P=(\frac{2134-1431}{2007-2003})t+1429\Rightarrow P=\frac{703}{4}t+1429$

So, the equation would be:

$P=175.75t+1429$

Now, we predict the number of people of the town in 2014:

$P_{2014}=175.75(14)+1429\Rightarrow P_{2014}=3889.5$

$\Rightarrow P_{2014}\approx3890$

So, there will be approximately 3890 people of the town in 2014.

3 0

1 year ago

Marsha had 8/9 yard of fabric. she cut it into 4 peices of equal length . how long was each piece

9966 [12]

8/9 = 0,8

0,8/4 = 0,2

so each piece was 0,2 yard long

4 0

4 years ago

Determine the standard form of the equation for the circle with center (h,k) = (-5 ½) and radius r =1

wariber [46]

Asuuing yo meant (h,k)=(-5,1/2)

equation is $(x-h)^2+(y-k)^2=r^2$
(h,k) is center and r=radious
given that (h,k)=(-5,1/2) and r=1
h=-5
k=1/2

$(x-(-5))^2+(y- \frac{1}{2} )^2=1^2$
$(x+5)^2+(y- \frac{1}{2} )^2=1$
if you wanted us to expand
x²+y^2+10x-y+25.25=1

8 0

3 years ago