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2 years ago

How does the unit circle allow the trigonometric functions to be defined for all real numbers instead of just for acute angles?

1 answer:

8 0

Every point in the unit circle is identified either by its coordinates $(x,y)$ or by the angle it forms with the x-axis, $\alpha$ .

The trigonometric functions associate with every angle $\alpha$ and the correspondant $(x,y)$ coordinates the two values

$\cos(\alpha)=x,\quad\sin(\alpha)=y$

This procedure can be done for every angle $\alpha$ , so you don't have to work with acute angles only.

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(60 points)

natka813 [3]

Answer:

Step-by-step explanation:

$2.\\(a-b)^2=a^2-2ab+b^2\\\\x^2-16x=-8\\\\x^2-2(x)(8)=-8\\\\\text{We have}\ 2ab=2(x)(8).\ \text{Therefore}\ b=8.\\\\x^2-2(x)(8)=-8\qquad\text{add}\ 8^2=64\ \text{to both sides}\\\\x^2-2(x)(8)+8^2=-8+64\\\\(x-8)^2=56$

$5.\\2x^2+x-1=2\qquad\text{subtract 2 from both sides}\\\\2x^2+x-3=0\\\\2x^2+3x-2x-3=0\\\\x(2x+3)-1(2x+3)=0\\\\(2x+3)(x-1)=0\iff 2x+3=0\ \vee\ x-1=0\\\\2x+3=0\qquad\text{subtract 3 from both sides}\\2x=-3\qquad\text{divide both sides by 2}\\\boxed{x=-\dfrac{3}{2}}\\\\x-1=0\qquad\text{add 1 to both sides}\\\boxed{x=1}$

$6.\\2x^2-4x=0\qquad\text{divide both sides by 2}\\\\x^2-2x=0\\\\x(x-2)=0\iff x=0\ \vee\ x-2=0\\\\\boxed{x=0}\\\\x-2=0\qquad\text{add 2 to both sides}\\\boxed{x=2}$

8 0

3 years ago

Help pls I don’t know anything

prohojiy [21]

Answer:

Step-by-step explanation:

first do this

6 0

1 year ago

Find the soultion(s) to the system of equations. Select all that apply

neonofarm [45]

Answer:

(0,-3)

(3,0)

Step-by-step explanation:

The solutions to the system of equations are where the two graphs cross

The first is at x=0 and y=-3

The second is at x=3 and y=0

3 0

3 years ago

A space shuttle travels at 2.6 x 10,000 feet per second. An hour is 3.6 x 1,000 seconds. This expression can be used to find the

guapka [62]

Answer:

7.22 feet

Step-by-step explanation:

From the question,

s = d/t................. Equation 1

Where s = speed of the space shuttle, d = distance traveled by the shuttle in an hour, t = time taken to travel the distance

make d the subject of the equation,

d = s×t.................... Equation 2

Given: s = 2.6×10000 feet per seconds, t = 1 hour = 3.6×1000 seconds.

Substitute these values into equation 2

d = (2.6×10000)/(3.6×1000)

d = 26000/3600

d = 7.22 feet.

Hence the shuttle travels 7.22 feet in an hour

6 0

3 years ago

Show your work:<br> (please dont answer with a link)

baherus [9]

Answer:

3) 8

4) 5.25 cups

Step-by-step explanation:

3) cross multiply:

36 × 10 = 360

45 × x = 45x

equate them both:

360 = 45x

divide both sides by 45

360 ÷ 45 = 8

x = 8

4) 8 people : 3 cups of flour

14 people : how many cups?

14 ÷ 8 = 1.75

to get from 8 people to 14 people we multiply by 1.75, so do the same thing to the 3 cups:

3 × 1.75 = 5.25 cups

5 0

2 years ago