In this window we are going to focus on the sine ratio. Remember that the sine of an angle is: sin  = length of opposite side/length of hypotenuse. As the hypotenuse is equal to 1, sin  = opposite side.

1.- Change the size of angle  and watch how the value given for sine changes.

2.- Check that the following relation is true for any value of Â: sin  = sin(Â+2kp), where k is a whole number.

3.- Is the value of the sine of angle  bounded (within a limited range)?

4.- Indicate whether sine has positive or negative values in each quadrant.

In this window we are going to focus on the cosine ratio. Remember that the cosine of an angle is: cos  = length of adjacent side/ length of hypotenuse. As the hypotenuse is equal to 1, cos  = adjacent side.

1.- Change the size of angle  and watch how the value given for cosine changes.

2.- Check that the following relation is true for any value of Â: cos  = cos(Â+2kp), where k is a whole number.

3.- Check that the following is true for any value of angle Â: 

cos²Â + sen²Â = 1

4.- Is the value of the cosine of angle  bounded (within a limited range)?

5.- Indicate whether cosine has positive or negative values in each quadrant.

6.- What is the size of angle  when cos  = 0?

In this window we are going to focus on the tangent ratio. Remember that the tangent of an angle is: tan  = length of opposite side/ length of adjacent side. 

1.- Change the size of angle  and watch how the value given for tangent changes.

Although we can use the formulae above to calculate the sine and cosine of any angle we cannot work out the tangent of certain angles: tan(p/2+ kp) does not exist when k is a whole number.

2.- Check that the following relation is true for any value of Â: tan  = tan(Â+kp), where k is a whole number.

3.- Is the value of the tangent of angle  bounded (within a limited range)?

4.- Indicate whether tangent has positive or negative values in each quadrant.

5.- What is the size of angle  when tan  = 0?

6.- What happens to the value of tan  when sin  = 0? What about when cos  = 0?

7.- How do the values of sin  , cos  and tan  relate to each other?

In this window we are going to focus on the cotangent ratio. The cotangent of an angle is: cot  = 1/tan Â.

Answer the following questions in your exercise book:

1.- Is the value of the cotangent of angle  bounded?

2.- Indicate whether cotangent has positive or negative values in each quadrant.

3.- What is the size of angle  when cot  = 0?

4.- What happens to the value of cot  when sin  = 0? What about when cos  = 0?

5.- What is the relation between the values of cot  and tan �

In this window we are going to focus on the secant ratio. The secant of an angle is: sec  = 1/cos   

2.- Check that the following relation is true for any value of Â: sec  = sec(Â+2kp), where k is a whole number.

3.- Is the value of the secant of angle  bounded?

4.- Indicate whether secant has positive or negative values in each quadrant.

5.- What is the size of angle  when sec  = 0?

6.- What happens to the value of sec  when sin  = 0? What about when cos  = 0?

7.- What is the relation between the values of sec  and cos �

In this window we are going to focus on the cosecant ratio. The cosecant of an angle is: cosec  = 1/sin   

1.- Change the size of angle  and watch how the value given for cosecant changes.

2.- Check that the following relation is true for any value of Â: cosec  = cosec(Â+2kp), where k is a whole number.

3.- Is the value of the cosecant of angle  bounded?

4.- Indicate whether cosecant has positive or negative values in each quadrant.

5.- What is the size of angle  when cosec  = 0?

6.- What happens to the value of cosec  when sin  = 0? 

7.- What is the relation between the values of cosec  and sin �