Chapter 13.2, Problem 51PPSE

Solution

i.

To complete: The given chart.

Given:

A chart is as follows:

  

Calculation:

Consider the following fact to complete the chart.

1. The $\cos \theta$ is negative in second and third quadrant. And positive in first and fourth quadrant.
2. The $\sin \theta$ is positive in first and second quadrant. And it is negative in third and fourth quadrant.

  

Conclusion:

Hence, the completed chart is given above.

ii.

To find: The quadrant in which the terminal side lies according to the given condition.

The terminal side will lies in the second quadrant.

Given:

The chart is as follows:

  

Calculation:

Consider the following completed graph.

  

According to the graph, the $\sin \theta$ is positive and a $\cos \theta$ is negative in the second quadrant. So, it can be concluded that the terminal side will lies in the second quadrant.

Conclusion:

Hence, the terminal side will lies in the second quadrant.

iii.

To explain: How the quadrant affects the sign of sine and cosine of that angle.

Quadrant determines the value’s sign of sine and cosine of angle.

Given:

A chart is as follows:

  

Calculation:

The sign of the value of the sine and cosine of a particular angle is determined by the quadrant. For example, if the $\cos \theta$ is positive in a certain quadrant, then the value of the cosine of the angle which lies in that quadrant will also be positive.

Conclusion:

Hence, the value’s sign of sine and cosine of an angle is determined by quadrant.