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1 year ago

Write the expression as the sine or cosine of an angle. Sin pi/3 cos pi/7 - sin pi/7 cos pi/3

Mathematics

1 answer:

Delicious77 [7]1 year ago

8 0

The expression can be written as : sin(π/3 - π/7)

<h3>what are trigonometric functions?</h3>

Trigonometric functions are functions that gives the relationship between the sides and angles of a triangle.

some of the trigonometric functions are sine, cosine, tangent.

Analysis:

Let A = π/3

B = π/7

If sin(A-B) = sinAcosB - cosAsinB

then sinπ/3cosπ/7 - sinπ/7cosπ/3 = sin(π/3 - π/7)

Learn more about Trigonometry : brainly.com/question/24349828

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Solve the equation for all real values of x.<br> cosxtanx - 2 cos x=-1

IceJOKER [234]

Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

<u>Step-by-step explanation:</u>

Here we have , $cosxtanx - 2 cos^2 x=-1$ . Let's solve :

⇒ $cosxtanx - 2 cos^2 x=-1$

⇒ $cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1$

⇒ $sinx = 2 cos^2 x-1$

⇒ $sinx = 2 (1-sin^2x)-1$

⇒ $sinx = 1-2sin^2x$

⇒ $2sin^2x+sinx-1=0$

By quadratic formula :

⇒ $sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}$

⇒ $sinx = \frac{-1 \pm3}{4}$

⇒ $sinx = \frac{1}{2} , sinx =-1$

⇒ $sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}$

⇒ $x=\frac{\pi}{6} , x=\frac{3\pi}{2}$

But at $x=\frac{3\pi}{2}$ we have equation undefined as $cos\frac{3\pi}{2}=0$ . Hence only solution is :

⇒ $x=\frac{\pi}{6}$

Since , $sin(\pi -x)=sinx$

⇒ $x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}$

Now , General Solution is given by :

⇒ $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$

Therefore , Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

3 0

2 years ago

The figure shows a line graph and two shaded triangles that are similar:

dlinn [17]

True:

3rd One

4th One

False: All of the others.

It's a straight line, so it is going to have straight qualities and straight inequalities throughout the graph.

8 0

2 years ago

The dot plot shows how many swimmers are in each line at a waterpark: Dot plot titled Swimmers in Line and labeled Number of Swi

nasty-shy [4]

The answer is median, because the data is skewed and there is an outlier.

3 0

2 years ago

Read 2 more answers

Help?

MAXImum [283]

Answer:

$32.39

Step-by-step explanation:

She has a 15-gallon tank and it has 1/5 a tank of gas left (so about 3/15)

Because she needs to refill it and already has 1/5, she'll only need to pay for 4/5 a tank of gas (12/15).

So the equation should be 12 times $2.699.

12 × 2.699 = 32.388

Then, round to the nearest cent.

32.388 = $32.39

Hope this helped !

5 0

1 year ago

Alvin is 7 years older than Elga. The sum of their ages is 97. What is Elga's age?

LenaWriter [7]

Elga's age = x

Alvin's age = x + 7

x + x + 7 = 97.

Simplify the left side of the equation

2x + 7 = 97.

Subtract 7 from each side

2x = 90.

Divide each side by 2

x = 45

Since x is equal to Elga's age, Elga is 45 years old

4 0

2 years ago