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here is my friends answer :

This unit focused on expanding previous knowledge from eleventh grade about trigonometry and its ratios. In the first two lessons, we learned about radians and how they relate to degrees.

Radians are a unit of measurement used in mathematics to quantify angles. Unlike degrees, which are commonly used in everyday life, radians provide a more natural and fundamental way to express angles in trigonometry. To understand radians, it's crucial to grasp the concept of a radian as a ratio between an arc and the radius of a circle. In a unit circle (a circle with a radius of 1), if an arc length along the circumference of the circle is equal to the radius, then the angle subtended by that arc at the center of the circle is defined as 1 radian. To put it simply, a radian is the angle subtended by an arc whose length is equal to the radius...

The ratio of the arc length to the radius of a circle give angle ? in radians: ? =arclength/radius

The relation between radians and degrees can be shown by converting degrees to radians:

? degrees (180/?rad)

It can also be shown by converting radians to degrees: ? rad(180/?rad)

It is important to note that radians can be expressed in two forms:

• Approximate form; Often when no special case is involved in a question, then an approximated answer with rounded decimals is expected.
• Exact form which involves a fraction and ? ? This is for special cases or exact values and is the most accurate and appropriate way to represent radians when and if possible.

Exact form derives from a unit circle that has four quadrants, and different fractions that each symbolize a specific special case...

\f\f\fCSCO = 71 6 2 Since 75 is in quadrant 3, and cine 6 is negative there, then csco will be negative too. Sin D = - 1 -> csco = - 2 2 : . The exact value is csco = - 2