y=2x−1 5x−4y=1 Is (1,1) a solution of system A.Yes B.No

If sin(x) = 5/13, and x is in quadrant 1, then tan(x/2) equals what?

Rufina [12.5K]

$x$ is in quadrant I, so $0$ , which means $0$ , so $\dfrac x2$ belongs to the same quadrant.

Now,

$\tan^2\dfrac x2=\dfrac{\sin^2\frac x2}{\cos^2\frac x2}=\dfrac{\frac{1-\cos x}2}{\frac{1+\cos x}2}=\dfrac{1-\cos x}{1+\cos x}$

Since $\sin x=\dfrac5{13}$ , it follows that

$\cos^2x=1-\sin^2x\implies \cos x=\pm\sqrt{1-\left(\dfrac5{13}\right)^2}=\pm\dfrac{12}{13}$

Since $x$ belongs to the first quadrant, you take the positive root ( $\cos x>0$ for $x$ in quadrant I). Then

$\tan\dfrac x2=\pm\sqrt{\dfrac{1-\frac{12}{13}}{1+\frac{12}{13}}}$

$\tan x$ is also positive for $x$ in quadrant I, so you take the positive root again. You're left with

$\tan\dfrac x2=\dfrac15$

4 0

3 years ago

you purchase 723 shares of Nike at $47.75 per share and one year later you are ready to sell your 723 shares for the current mar

Anettt [7]

The answer to this question is "you gained profit". The amount of money you gain from selling the stocks now is higher compared to the amount you spent a year ago. The amount you gain from the shares is ($62.25) x 723 = $45006.75. The amount you spent last year is ($47.75) x 723 = $34523.25. The difference between the values is $10483.47. Thus, you gained $10483.47.

5 0

3 years ago

Determine the smallest integer value of x in the solution 4x-9 ≥ 17

jeka94

Answer:

6.5

Step-by-step explanation:

calculator

3 0

2 years ago

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McKenzie works for a catering company she is making ice tea for an upcoming event for each container of tea she uses 16 tea bags

never [62]

64 divided by 16= 4

3x4=12

if Mckenzie uses 64 tea bags she will need to use 12 cups of sugar

7 0

3 years ago

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I’m very bored and I want to learn something. Tell me something cool like a fun fact or a joke and the best one gets Brainliest!

lbvjy [14]

Did you know that horses sleep standing up and also laying down
Horses also can’t burp or vomit
Horses are measured in hands which is about four fingers sideways
There are no such thing as white horses horses that are white with gray Noses are called greats horses that are white with pink skin are called cremello

7 0

2 years ago

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​ y=2x−1 5x−4y=1 ​ Is (1,1) a solution of system A.Yes B.No

y=2x−1 5x−4y=1 Is (1,1) a solution of system A.Yes B.No