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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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Write the formula for the parabola that has x- intercepts (3,0) and (8,0), and y- intercept (0,−2)
alexira [117]

Answer:x^2-5x=-12(y+2)

Step-by-step explanation:

Given

Parabola has x-intercept has (3,0) and (8,0)

and Y-intercept as (0,-2)

Now the general equation of parabola is

y=ax^2+bx+c\quad \ldots(i)

Substitute  (0,-2) in (i) we get

-2=c

Now substitute (3,0) in equation (i)

0=a(3)^2+3b-2\quad \ldots(ii)

Now substitute (8,0) in equation (i)

0=a(8)^2+8b-2\quad \ldots(iii)

Solving (ii) and (iii) we get

a=\frac{-1}{12}\ \text{and}\ b=\frac{5}{12}

therefore

y=\frac{-x^2}{12}+\frac{5x}{12}-2

12y=-x^2+5x-24

5 0
3 years ago
A Pringles chip can has a diameter of about 2.8 inches and a height of about 11.8 inches (close to real measurement) what volume
NARA [144]

Answer:

72.66 in³

Step-by-step explanation:

The volume of a cylinder of radius r and height h is given by V = πr²h.

Here we have  V = πr²h = π([2.8]/2 in)²(11.8 in) = π(1.96 in²)(11.8 in) = 23.1 π in³, or approximately 72.66 in³

6 0
3 years ago
-17+4a<br><br> Please solve.
ikadub [295]

Answer:

-17+4a=0

-17= -4a(-,-=+)

a=17/4

7 0
2 years ago
Read 2 more answers
What is Q=R+Rst; solve for s
oksano4ka [1.4K]

Step-by-step explanation:

q=r+rst

Rewrite the equation as 

r+rst=q

Subtract r from both sides of the equation.

r st=q−r

Divide each term by rt

(r st )/rt=(q/rt)−(r/rt)

Cancel the common factor.

(

s=(q/rt)−1/t

6 0
3 years ago
Carlos earns $11 per hour at his job. Let x represent the number of hours he worked in May. Let y represent the number of hours
Firlakuza [10]

11x+11y

11(x+y)

Explanation

Step 1

Let

Carlos earns == 11 per hour

x represents the number of hours he worked in May

the,

the amount he earned in Mayis

11\cdot x=11x

y represent the number of hours he worked in June.

the amount he earned in June was

11\cdot y=11y

Step 2

the amount of money he earned is May and June is the sum of the values

\begin{gathered} \text{total}= \\ 11x+11y \\ \text{if we factorize 11} \\ 11(x+y) \end{gathered}

I hope this helps you

5 0
10 months ago
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