Which conclusion can be drawn from the graph data?

Why tan(π/4) = 1 can you explain it simply? Also can we use it with cos, cot, sin, sec and cosec? Thanks! please, please dont wr

damaskus [11]

Answer:

1) tan π/4 = 1

2) cos π/4 = 0.7071

3) cot π/4 = 1

4) sin π/4 = 0.7071

5) sec π/4 = 1.4142

6) cosec π/4 = 1.4142

Step-by-step explanation:

Angle π is in radians

But converting to degree, it is;

π = 180˚

Thus; π/4 = 180/4 = 45°

Thus;

1) from calculator; tan π/4 = tan 45° = 1

2) from calculator, cos π/4 = cos 45° = 0.7071

3) cot is equivalent to 1/tan

Thus; cot π/4 = 1/(tan π/4) = 1/tan 45 = 1/1 = 1

4) from calculator, sin π/4 = sin 45° = 0.7071

5) sec in trigonometry is equivalent to 1/cos.

Thus;

sec π/4 = 1/cos π/4 = 1/cos 45° = 1/0.7071 = 1.4142

6) cosec in trigonometry is equivalent to 1/sin

Thus;

cosec π/4 = 1/sin π/4 = 1/sin 45° = 1/0.7071 = 1.4142

7 0

3 years ago

Two pumps are filling a pool. One of them is high power and can fill the pool alone in 2 hours less time than the other can do s

slega [8]

Answer:

4 hours

Step-by-step explanation:

Let x minutes be the time needed for the powerful pomp to fill the pool. Then x+120 minutes is the time needed to the other pomp to fill the pool. The powerful pomp fills $\dfrac{1}{x}$ of the pool in a minute and the other pomp fills $\dfrac{1}{x+120}$ of the pool in a minute. Filling together, they fill $\dfrac{1}{x}+\dfrac{1}{x+120}$ of the pool in a minute and

$144\cdot \left(\dfrac{1}{x}+\dfrac{1}{x+120}\right)$

in 144 minutes.

Thus,

$144\cdot \left(\dfrac{1}{x}+\dfrac{1}{x+120}\right)=1.$

Solve this equation:

$\dfrac{144(x+120)+144x}{x(x+120)}=1,\\ \\144x+144\cdot 120+144x=x^2+120x,\\ \\x^2-168x-17280=0,\\ \\D=(-168)^2-4\cdot (-17280)=97344,\\ \\x_{1,2}=\dfrac{-(-168)\pm \sqrt{97344}}{2}=\dfrac{168\pm 312}{2}=-72,\ 240.$

Hence, it is needed the powerful pomp 240 minutes = 4 hours to fill the pool.

4 0

3 years ago

How would you find the vertices of an image of a figure was rotated 270 degrees clockwise? 15 POINTS! DESPERATE

boyakko [2]

Rotation Coordinate Notation About the Origin:

90–degree counterclockwise: (x, y) → (-y, x)

180–degree counterclockwise: (x, y) → (-x, -y)

270–degree counterclockwise: (x, y) → (y, -x)

Use this to help you..

Example -

The vertices of a triangle are

( 1 , 3 ) ( 3 , -4 ) , ( - 6 , -8 )

270 degrees , clockwise , rotated from origin ( x , y ) - ( y , -x )

The first vertice = ( 1 , 3 )

after rotation - ( 3 , - 1 )

The second vertice = ( 3 , -4 )

After rotation - ( -4 , -3 )

The third vertice = ( -6 , - 8 )

After rotation - ( -8 , 6 )

Hope my answer helps!

5 0

4 years ago

Read 2 more answers

Is x^(-2)+5 a polynomial expression? Why or why not? Read More >>

Mariulka [41]

Well.. a polynomial expression is an expression that has 3 or more different algebraic terms.

Algebraic terms can be: x^2, 2x, or x^3

One example is: x^2 + x^3 - 7y

Since x^(-2)+5 only has one algebraic term, which is x^(-2), this is not a polynomial.

4 0

3 years ago

The area of a garden is 15 3/4 square feet. If the length is 7 5/7, what is the width in feet?

disa [49]

Answer:

441/216 feets

Step-by-step explanation:

15 3/4=63/4

7 5/7=54/7

-----------------

(63/4)/(54/7)

(63/4)(7/54)

441/216

8 0

3 years ago

Read 2 more answers