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lara [203]
2 years ago
11

 Find sin2x, cos2x, and tan2x if sinx=-15/17 and x terminates in quadrant III

Mathematics
1 answer:
vodka [1.7K]2 years ago
7 0

Given:

\sin x=-\dfrac{15}{17}

x lies in the III quadrant.

To find:

The values of \sin 2x, \cos 2x, \tan 2x.

Solution:

It is given that x lies in the III quadrant. It means only tan and cot are positive and others  are negative.

We know that,

\sin^2 x+\cos^2 x=1

(-\dfrac{15}{17})^2+\cos^2 x=1

\cos^2 x=1-\dfrac{225}{289}

\cos x=\pm\sqrt{\dfrac{289-225}{289}}

x lies in the III quadrant. So,

\cos x=-\sqrt{\dfrac{64}{289}}

\cos x=-\dfrac{8}{17}

Now,

\sin 2x=2\sin x\cos x

\sin 2x=2\times (-\dfrac{15}{17})\times (-\dfrac{8}{17})

\sin 2x=-\dfrac{240}{289}

And,

\cos 2x=1-2\sin^2x

\cos 2x=1-2(-\dfrac{15}{17})^2

\cos 2x=1-2(\dfrac{225}{289})

\cos 2x=\dfrac{289-450}{289}

\cos 2x=-\dfrac{161}{289}

We know that,

\tan 2x=\dfrac{\sin 2x}{\cos 2x}

\tan 2x=\dfrac{-\dfrac{240}{289}}{-\dfrac{161}{289}}

\tan 2x=\dfrac{240}{161}

Therefore, the required values are \sin 2x=-\dfrac{240}{289},\cos 2x=-\dfrac{161}{289},\tan 2x=\dfrac{240}{161}.

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Can someone help with this one?
Vedmedyk [2.9K]

Answer:

(a) 0.05 minutes per calorie burned

(b) Slope = 20

Step-by-step explanation:

(a) If 200 calories are burned in 10 minutes...then what about 1 calorie

; 1/200 × 10 = 0.05 minutes

(b) Slope of the graph...;just take any two points on the graph...which are (10;200) and (20;400)

Slope = (400 - 200) ÷ (20 - 10)

;Slope = 200 ÷ 10

;Slope = 20

7 0
3 years ago
1/4x – 2 = 3/8 Please show an equation and work. :)
Julli [10]
1/4x - 2 = 3/8

First, to start solving this, we can rearrange our fraction. Let's take 1/4x and change it to x/4. Why? Well, a variable can also be considered as the number 1.
\frac{x}{4} - 2 =  \frac{3}{8}

Second, now we can continue solving for our variable (x). Let's add 2 to each side.
\frac{x}{4} =  \frac{3}{8} + 2

Third, let's simplify 3/8 + 2. (3/8 + 2 = 2.375 =19/8)
\frac{x}{4} =  \frac{19}{8}

Fourth, continue trying to get the variable by itself. Multiply each side by 4.
x =  \frac{19}{8} \times 4

Fifth, let's simplify 19/8 × 4. This is simple. Leave the denominator be and just do 19 × 4, which equals 76.
x =  \frac{76}{8}

Sixth, our final step is to simplify our fraction. To do so, we will need to list the factors of the numerator and denominator and find the greatest common factor (GCF).

Factors of 76: 1, 2, 4, 19, 38, 76
Factors of 8: 1, 2, 4, 8

Since 4 is our first common factor, it is considered our GCF.

Seventh, now let's divide. Divide both the numerator and denominator by the GCF (4) to create our new simplified fraction.
76 \div 4 = 19 \\ 8 \div 4 = 2

Answer in fraction form: \fbox {x = 19/2}
Answer in decimal form: \fbox {x = 9.5}
8 0
3 years ago
George invited 65 students in his school to volunteer at a charity race. 39 of the students signed up to volunteer. What percent
mr Goodwill [35]

Answer:

60%

Step-by-step explanation:

Divide the amount of people who showed up by the total invited...

39/65 = 0.6

To convert a decimal to a percent, multiply the decimal by 100%...

0.6(100%) = 60%

8 0
3 years ago
What is 0.15 in word form
Molodets [167]
0.15 in word form is fifteen hundredths 

*Hope I Helped*
8 0
3 years ago
Yall help me?please and thank you
aksik [14]
It would be 27/8 = 3 3/8 next 18/5 = 3 3/5 after that 19/6 = 3 1/6 lastly 35/4 = 8 3/4
Hope this helped!

3 0
3 years ago
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