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4 years ago

Sin(x) + sin(3x) = 4 sin(x) cos^2(x) Prove the identity.

1 answer:

6 0

$\bf \textit{Sum to Product Identities} \\\\ sin(\alpha)+sin(\beta)=2sin\left(\cfrac{\alpha+\beta}{2}\right)cos\left(\cfrac{\alpha-\beta}{2}\right)\leftarrow \textit{we'll use this one} \\\\\\ sin(\alpha)-sin(\beta)=2cos\left(\cfrac{\alpha+\beta}{2}\right)sin\left(\cfrac{\alpha-\beta}{2}\right) \\\\\\ \stackrel{\textit{symmetry identity}}{cos(-\theta )=cos(\theta )} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf sin(x)+sin(3x)=\underline{4sin(x)cos^2(x)} \\\\[-0.35em] ~\dotfill\\\\ sin(x)+sin(3x)\implies 2sin\left( \cfrac{x+3x}{2} \right)cos\left( \cfrac{x-3x}{2} \right) \\\\\\ 2sin\left( \cfrac{4x}{2} \right)cos\left( \cfrac{-2x}{2} \right)\implies 2sin(2x)cos(-x)\implies 2\boxed{sin(2x)} cos(x) \\\\\\ 2\boxed{2sin(x)cos(x)} cos(x)\implies \underline{4sin(x)cos^2(x)}$

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A slide 4.1 meters long makes an angle of 35° with the ground. To the nearest tenth of a meter, how far above the ground is the

Artemon [7]

Hey there! I'm happy to help!

We want to figure out what x is. Let's use a trigonometric ratio of our 35 degree angle to find it.

We see that x is opposite of the 35 degree angle. We also see that our hypotenuse 4.1 m. The hypotenuse is always across from the right angle.

The trigonometric ratio that deals with opposite and hypotenuse is the sine, which is the opposite divided by the hypotenuse. This gives us the following equation.

$sin35=\frac{x}{4.1}$

We want to solve for x, so we simply multiply both sides 4.1

$x=4.1(sin35)$

If we evaluate this on our calculators, we get 2.351663389......

We round this to the nearest tenth, giving us 2.4 m.

Have a wonderful day! :D

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3 years ago

You are creating strings picking letters from the English alphabet at random. What is the probability that your randomly created

White raven [17]

There are 4 positions in the string that each have 25 choices (any letter in the English alphabet except A) and the other positions are filled with A, so there are 25⁴ possible strings containing exactly 7 A's.

Overall, there are 26¹¹ possible strings of length 11.

Then the probability of randomly generating a string containing exactly 7 A's is

25⁴ / 26¹¹ ≈ 0.000000000106427

8 0

3 years ago

Find the measure of each angle indicated

sergey [27]

Step-by-step explanation:

90+115+65=270

360-270=90

Answer:

U=90°

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3 years ago

If arctan(3/5)=K Tan(k)=?

hichkok12 [17]

$arctan(x)=y$

this function is the inverse function of tan...

$arctan(x)=tan^{-1}(x)$

then...

$x=tan(y)$

in this case

$arctan(\frac{3}{5})=K$

$\frac{3}{5}=tan(K)$

$\boxed{\boxed{tan(K)=\frac{3}{5}}}$

3 0

3 years ago

Read 2 more answers

Wawa pays $100 for 5 hours work. 7-11 pays $200 for 9 hours work. Which job should u take?

yawa3891 [41]

Obviously 7-11 is you’re looking for more profit over free time. Simple math here, 5x2=10 meaning you’d get the same amount of pay while working one extra hour at Wawa’s. That hour extra may not seem like much but it adds up over time.

8 0

3 years ago