I need help with these questions (see image). Please show workings.​

r =

Step-by-step explanation:

h bisects l at right angles.

There is a right triangle formed with legs h and l and hypotenuse r

Using Pythagoras' identity, then

r² = ( l )² + h²

   = l² + h² ← factor out

    = (l² + 4h²)

Take the square root of both sides

r = =

Step-by-step explanation:

Connect the endpoints of the with the center. The formed triangle is isosceles with sides l, r and r.

The height of the triangle h, is the distance between the center of the circle and the midpoint of the chord.

As per Pythagorean theorem we have:

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: