Question

Find the values of the six trigonometric functions of  with the given constraint.

 

lies in Quadrant II.

Answer 1

Step 1:

The trigonometric function is , where lies in quadrant II.

Right angled triangle definition of trigonometric function .

Opposite side = 3 and hypotenuse = 5.

Pythagorean theorem:

For right angled triangle, square of hypotenuse is equal to sum of squares of other two sides.  

Substitute opposite side = 3 and hypotenuse = 5 in above theorem.

Adjacent side = 4.

Sine and Cosecant functions are positive and remaining trigonometric functions are negative.

Since, lies in quadrant II.

Solutions :

, , , , and .