Question 1: Find the values of the other five trigonometric functions in each of the following:

i) , in Quadrant III ii) , in Quadrant II

iii) , in Quadrant III iv) , in Quadrant I

Answer:

i) , in Quadrant III

We know

in Quadrant III, is negative

We know,

Also

Now

In Q III, is negative

ii) is in Quadrant II

We know

In Quadrant II, is positive and is negative

iii) , in Quadrant III

In Quadrant III, is negative

Also

iv) , in Quadrant I

In Quadrant I, is positive

and

Question 2: If and lies in Quadrant II, find the value of .

Answer:

in Quadrant II

in Quadrant II is negative

Question 3: If and and , find the value of .

Answer:

Given and and

in Quadrant II and in Quadrant III

in Quadrant II is negative

in Quadrant III is negative

Question 4: If , and lies in the fourth quadrant, find and .

Answer:

in Quadrant IV

in Quadrant IV, is positive

Since

Question 5: If and , find the value of the five trigonometric functions and hence evaluate .

Answer:

Given and

in Quadrant III

In Quadrant III, is negative