What is the sum of the first eight terms of the geometric series?

Find the exact value of each trigonometric function for the given angle θ.

Kay [80]

Answer:

$\sin (240^\circ)=-\dfrac{\sqrt{3}}{2},\cos (240^\circ)=-\dfrac{1}{2},\tan (240^\circ)=\sqrt{3},\cot (240^\circ)=\dfrac{1}{\sqrt{3}},\sec (240^\circ)=-2,\csc (240^\circ)=\dfrac{2}{\sqrt{3}}.$

Step-by-step explanation:

The given angle is 240 degrees.

We need to find the exact value of each trigonometric function for the given angle θ.

Since $\theta=240$ , it means θ lies in 3rd quadrant. In 3d quadrant only tan and cot are positive.

$\sin (240^\circ)=\sin (180^\circ+60^\circ)=-\sin (60^\circ)=-\dfrac{\sqrt{3}}{2}$

$\cos (240^\circ)=\cos (180^\circ+60^\circ)=-\cos (60^\circ)=-\dfrac{1}{2}$

$\tan (240^\circ)=\tan (180^\circ+60^\circ)=\tan (60^\circ)=\sqrt{3}$

$\cot (240^\circ)=\cot (180^\circ+60^\circ)=\cot (60^\circ)=\dfrac{1}{\sqrt{3}}$

$\sec (240^\circ)=\sec (180^\circ+60^\circ)=-\sec (60^\circ)=-2$

$\csc (240^\circ)=\csc (180^\circ+60^\circ)=-\csc (60^\circ)=-\dfrac{2}{\sqrt{3}}$

Therefore, $\sin (240^\circ)=-\dfrac{\sqrt{3}}{2},\cos (240^\circ)=-\dfrac{1}{2},\tan (240^\circ)=\sqrt{3},\cot (240^\circ)=\dfrac{1}{\sqrt{3}},\sec (240^\circ)=-2,\csc (240^\circ)=-\dfrac{2}{\sqrt{3}}.$

8 0

3 years ago

16^5/4•16^1/4/(16^1/2)^2

Kazeer [188]

Answer:

The simplified expression is 16^-1/6

Step-by-step explanation:.

16^5/4•16^1 /4/ (16^1/2)^2

The dot means multiplication. The expression is rewritten as

16^5/4 × 16^1/4 / (16^1/2)^2

Recall the following rules of indices

1) y^a × y^b = y^(a+b)

2) (y^a)^b = y^ab

y^b/ y^a = y^(b-a)

Applying these rules of indices

16^5/4 × 16^1/4= 16^((5/4×1/4) = 16^((5/16)

(16^1/2)^2= 16^ 1/2×2 = 16^1 = 16

Therefore

16^5/4 × 16^1/4 / (16^1/2)^2

= 16^(5/16) /16

=16^(5/6) × 16^-1

= 16^ (5/6)-1

= 16^-1/6)

,The simplified expression is 16^-1/6

8 0

3 years ago

how to find the area of each circle. use a calculator value of pi. round the answer to the nearest tenth

tankabanditka [31]

Answer:

A = 201.0 mi^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

We know that r = 8

A = (3.14) *8^2

A = 3.14 * 64

A = 200.96 mi ^2

Rounding to the nearest tenth

A = 201.0 mi^2

8 0

3 years ago

Read 2 more answers

Which of the following represents the area of a rectangle whose length is 5x − 3 and whose width is x + 7?

Nookie1986 [14]

Answer : option C, 5x2 + 32x − 21

In the rectangle, the length = 5x - 3 and width = x + 7

We know the formula for area of rectangle = length * width

Area of rectangle = (5x-3)(x+7)

WE multiply it using FOIL method

F - First terms, 5x * x = $5x^2$

O- Outer terms, 5x * 7 = 35x

I - Inner terms, -3 * x= -3x

L - Last terms, -3 * 7 = -21

Now we add all the terms

$5x^2 +35x -3x -21$

combine like terms

$5x^2 +32x -21$

So area of a rectangle = $5x^2 +32x -21$

4 0

3 years ago

Need help lease!!!!!!!

Viefleur [7K]

(11)

the equation of a line in point- slope form is

y = mx + c ( m is the slope and c the y-intercept

thus y = 4x + 3 ← in slope-intercept form

the equation of a line in point- slope form is

y - b = m(x - a ) ( m is slope and (a, b ) a point on the line )

thus y - 3 = 4 ( x - 0 ) or y - 3 = 4x ← in point- slope form

the equation of a line in standard form is

Ax + By = C ( a is a positive integer and B, C are integers

rearrange y - 3 = 4x into this form

4x - y = - 3 ← in standard form

(12)

y = - 2x - 1 ← in slope-intercept form

y + 1 = - 2x ← in point- slope form

2x + y = - 1 ← in standard form

8 0

3 years ago