What's the exact value of tan(-4pi/3)

Use the given information to find the exact value of the trigonometric function

eimsori [14]

$\begin{gathered} \csc \theta=-\frac{6}{5} \\ \tan \theta>0 \\ \cos \frac{\theta}{2}=\text{?} \end{gathered}$

Half Angle Formula

$\cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}}$ $\tan \theta>0\text{ and csc}\theta\text{ is negative in the third quadrant}$ $\begin{gathered} \csc \theta=-\frac{6}{5}=\frac{r}{y} \\ x^2+y^2=r^2 \\ x=\pm\sqrt[\square]{r^2-y^2} \\ x=\pm\sqrt[\square]{6^2-(-5)^2} \\ x=\pm\sqrt[\square]{36-25} \\ x=\pm\sqrt[\square]{11} \\ \text{x is negative since the angle is on the 3rd quadrant} \end{gathered}$ $\begin{gathered} \cos \theta=\frac{x}{r}=\frac{-\sqrt[\square]{11}}{6} \\ \cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}} \\ \cos \frac{\theta}{2}is\text{ also negative in the 3rd quadrant} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{1+\frac{-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{\frac{6-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}} \\ \\ \end{gathered}$

Answer:

$\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}$

Checking:

$\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{ (3rd quadrant)} \end{gathered}$

Also,

$\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}$

The answer is none of the choices

7 0

10 months ago

What is the circumference?

bonufazy [111]

1 : the perimeter of a circle The circle measures 22 inches in circumference. 2 : the external boundary or surface of a figure or object : periphery from the center to the circumference of the sphere.

6 0

1 year ago

2<br> .<br> 2<br> 12n = 42<br> NEED HELP ASAP⬆️

Anni [7]

Answer:

6

—————

n + 8

Step-by-step explanation:

Step by Step Solution:

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STEP

1

:

Equation at the end of step 1

((12•(n3))-(24•(n2))) (12n-42)

—————————————————————•———————————————————

(((4•(n2))-22n)+28) ((6•(n3))+(24•3n2))

STEP

2

:

Equation at the end of step

2

:

((12•(n3))-(24•(n2))) (12n-42)

—————————————————————•——————————————————

(((4•(n2))-22n)+28) ((2•3n3)+(24•3n2))

STEP

3

:

12n - 42

Simplify ——————————

6n3 + 48n2

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

12n - 42 = 6 • (2n - 7)

STEP

5

:

Pulling out like terms

5.1 Pull out like factors :

6n3 + 48n2 = 6n2 • (n + 8)

Equation at the end of step

5

:

((12•(n3))-(24•(n2))) (2n-7)

—————————————————————•————————

(((4•(n2))-22n)+28) n2•(n+8)

STEP

6

:

Equation at the end of step

6

:

((12•(n3))-(24•(n2))) (2n-7)

—————————————————————•————————

((22n2-22n)+28) n2•(n+8)

STEP

7

:

Equation at the end of step

7

:

((12•(n3))-(23•3n2)) (2n-7)

————————————————————•————————

(4n2-22n+28) n2•(n+8)

STEP

8

:

Equation at the end of step

8

:

((22•3n3) - (23•3n2)) (2n - 7)

————————————————————— • ————————————

(4n2 - 22n + 28) n2 • (n + 8)

STEP

9

:

12n3 - 24n2

Simplify ——————————————

4n2 - 22n + 28

STEP

10

:

Pulling out like terms

10.1 Pull out like factors :

12n3 - 24n2 = 12n2 • (n - 2)

STEP

11

:

Pulling out like terms

11.1 Pull out like factors :

4n2 - 22n + 28 = 2 • (2n2 - 11n + 14)

Trying to factor by splitting the middle term

11.2 Factoring 2n2 - 11n + 14

The first term is, 2n2 its coefficient is 2 .

The middle term is, -11n its coefficient is -11 .

The last term, "the constant", is +14

Step-1 : Multiply the coefficient of the first term by the constant 2 • 14 = 28

Step-2 : Find two factors of 28 whose sum equals the coefficient of the middle term, which is -11 .

-28 + -1 = -29

-14 + -2 = -16

-7 + -4 = -11 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -4

2n2 - 7n - 4n - 14

Step-4 : Add up the first 2 terms, pulling out like factors :

n • (2n-7)

Add up the last 2 terms, pulling out common factors :

2 • (2n-7)

Step-5 : Add up the four terms of step 4 :

(n-2) • (2n-7)

Which is the desired factorization

Canceling Out :

11.3 Cancel out (n-2) which appears on both sides of the fraction line.

Equation at the end of step

11

:

6n2 (2n - 7)

—————— • ————————————

2n - 7 n2 • (n + 8)

STEP

12

:

Canceling Out

12.1 Cancel out (2n-7) which appears on both sides of the fraction line.

Canceling Out :

12.2 Canceling out n2 as it appears on both sides of the fraction line

Final result :

6

—————

n + 8

8 0

3 years ago

9 If 10,000 Birr is invested for 6 years at annual simple interest rate of 16%, what will be interest earned and annount of the

svp [43]

9514 1404 393

Answer:

(C) 9600, 19600

Step-by-step explanation:

The interest is given by ...

I = Prt

I = 10,000×0.16×6 = 9,600 . . . interest earned

The amount of the investment is the total of the principal and the interest earned:

10,000 +9,600 = 19,600 . . . amount of investment after 6 years

7 0

2 years ago

Pepe tenía dinero ahorrado en su alcancia pero le retiró $75 para comprar un jugete. Ahora tiene $250 en su alcancia ¿Cuánto din

gregori [183]

El tenia $325

$250+$75=$325

Espero q te ayude :)

4 0

2 years ago