Cosecant and Sine Function Concepts

This video tutorial explains how to solve trigonometric equations involving cosecant theta without using a calculator. It covers two main problems: solving cosecant theta equals square root two and cosecant theta equals negative two, using both the unit circle and reference triangles. The tutorial emphasizes understanding the reciprocal relationship between sine and cosecant and demonstrates how to find solutions in different quadrants of the unit circle. It also highlights the importance of reference triangles in identifying angles with specific trigonometric values.

What is the reciprocal of cosecant theta?

• Cosine theta

• Sine theta

• Secant theta

• Tangent theta

In which quadrants is sine theta positive?

• First and second

• Second and third

• Third and fourth

• First and fourth

What is the rationalized form of 1 divided by square root two?

• One divided by two

• Two divided by square root two

• Square root two divided by two

• Square root two

Which angles correspond to a sine value of square root two divided by two?

• Pi over two and three pi over two

• Pi over four and three pi over four

• Pi over six and five pi over six

• Pi over three and two pi over three

What is the cosecant of pi over four?

• Square root two

• Square root three

• One

• Two

In which quadrants is cosecant theta negative?

• First and fourth

• Third and fourth

• Second and third

• First and second

What is the sine value when cosecant theta equals negative two?

• Negative square root three

• Negative one half

• Negative square root two

• Negative two

Which angles have a sine value of negative one half?

• Pi over four and three pi over four

• Pi over three and two pi over three

• Seven pi over six and eleven pi over six

• Pi over six and five pi over six

What is the reference angle for a sine value of one half?

• Pi over six

• Pi over four

• Pi over three

• Pi over two

How do you find the angle in radians for a full revolution minus pi over six?

• Five pi over six

• Eleven pi over six

• Seven pi over six

• Three pi over six