If (cos)x= 1/2 what is sin(x) and tan(x)? Explain your steps in complete sentences.

Answers

Answer 1

Answer: The correct answers are:
1) sin(x) = $( √(3) )/(2)$
2) tan(x) = $√(3)$

Explanation:
Given:
$cos(x) = (1)/(2)$

Step 1:
Since, according to the Trigonometric identity:
$sin^2(x) + cos^2(x) = 1$ -- (1)

Step 2:
Plug in the value of cos(x) in equation (1):
$sin^2(x) + ( (1)/(2) )^2 = 1 \n sin^2(x) + (1)/(4) = 1 \n sin^2(x) = (3)/(4)$

Step 3:
Take square-root on both sides:
$√(sin^2(x)) = \sqrt{(3)/(4)}$

sin(x) = $( √(3) )/(2)$

Now to find the tan(x), we would use the following formula:

tan(x) = $(sin(x))/(cos(x))$ --- (2)

Plug in the values of sin(x) and cos(x) in equation (2):
tan(x) = $( ( √(3) )/(2) )/( (1)/(2) )$

Hence tan(x) = $√(3)$

Answer 2

Answer:

Answer:

The value of $\sin x=(√(3))/(2)$

The value of $\tan x=√(3)$

Step-by-step explanation:

Given = $\cos x=(1)/(2)$

To find : $\sin x=?$ and $\tan x=?$

Solution:

We know that, if the cosine function of an angle is $(1)/(2)$ then the angle is equal to the 60°.

$\cos x=(1)/(2)$

x = 60°

The value of the :

$\sin x=\sin 60^o=(√(3))/(2)$

We know that ratio of sine function to the cosine function is equal tto the tangent

$\tan x=(\sin x)/(\cos x)=((√(3))/(2))/((1)/(2))=√(3)$

The value of $\sin x=(√(3))/(2)$

The value of $\tan x=√(3)$

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Pls help I need help why are

Answers

I believe they are about the similar in shape unless you have answers to them?

Answer:

Both of their bases are parallel

Step-by-step explanation:

Which is the completely factored form of 12x3 – 60x2 + 4x – 20?

Answers

$12x^3 - 60x^2 + 4x - 20 \n \n GCF = 4 \n \n 4( (12x^3)/(4) + (-60x^2)/(4) + (4x)/(4) - (20)/(4)) \n \n 4(3x^3 - 15x^2 + x - 5) \n \n 4(3x^2(x - 5) + (x - 5)) \n \n 4(x - 5)(3x^2 + 1) \n \n$

The final result is: 4(x - 5)(3x² + 1).

Which of the following fractions would become a repeating decimal?a.1/8
b.3/4
c.27/36
d.7/9
e.5/8

Answers

Because we work in a base 10 number system, any denominator that can be expressed as a multiple of 2s 5s and 10s will not be infinite and therefore not repeating. 1/8 is 1/(2*2*2) which is .125. 3/4 is 3/(2*2) which is .75. 27/36 is a tricky one because it's not in simplest form. You can divide the top and bottom by 9 to get 3/4 which we already know is .75. 5/8 is 5/(2*2*2) which is .625. That leaves 7/9. 9 cannot be expressed as a multiple of 2s and 5s ad tens so it must be that one. 7/9 is .777777 repeating.

Which equation is quadratic in form?2(x + 5)2 + 8x + 5 + 6 = 0
x6 + 6x4 + 8 = 0
7x6 + 36x3 + 5 = 0
4x9 + 20x3 + 25 = 0

Answers

Answer: Option 1 is correct.

Step-by-step explanation:

As we know that the quadratic form needs the highest degree to be '2' only.

So,

In Option 1, we have ,

$2(x+5)^2+8x+5+6=0\n\n2(x^2+10x+25)+8x+11=0\n\n2x^2+20x+50+8x+11=0\n\n2x^2+28x+61=0\n\n\text{ Hence , it is the required quadratic form. }$

Hence, Option 1 is correct.

Answer:

Option 1 is correct.

Step-by-step explanation:

Given the equations we have to choose the equation which is in quadratic form.

Quadratic form of equation is of the the form

$ax^2+bx+c=0$

The quadratic form needs the degree to be '2' only.

Option 1:

$2(x+5)^2+8x+5+6=0$

$(a+b)^2=a^2+b^2+2ab$

$2(x+5)^2+8x+5+6=0\n\n2(x^2+10x+25)+8x+11=0\n\n2x^2+20x+50+8x+11=0\n\n2x^2+28x+61=0\n\n\text{which is of degree 2.}$

$\text{Hence , it is the required quadratic form. }$

Hence, Option 1 is correct.

Rest three equations are not of degree 2 therefore not in quadratic form.

The hypotenuse of aright triangle is 10 cm.

One of the side lengths is 8 cm.

What is the length of the other side?

Answers

Answer:

6 cm

Step-by-step explanation:

We can use the Pythagorean Theorem to find the length of the missing side.

The Pythagorean Theorem states that the hypotenuse of a right triangle will be $a^2 + b^2$ , where a and b are the leg lengths.

Together, we get the formula $a^2 + b^2 = c^2$ .

Since we know the hypotenuse (c) and one of the sides (let's say a), we can find the missing side (b) by substituting inside the equation.

$8^2 + b^2 = 10^2\n\n64 + b^2 = 100\n\nb^2 = 100-64\n\nb^2 = 36\n\nb = √(36)\n\nb=6$

So the missing side is 6 cm long.

Hope this helped!

Answer:

6 cm

Step-by-step explanation:

use Pythagorean theorem a² + b² = c²

let c = 10 cm , b = 8 cm

plug in values

a² + 8² = 10²

a² = 10² - 8²

a = $√(10^2 - 8^2)$

a = 6 cm

Find the value of y if given: 20y-2, 17y +3, 5x + 8, 21x

Answers

20y-2=
20y=2
20y/20=2/20
y=0.1

17y +3=
17y=-3
17y/17=-3/17
y=-0.176

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