SKETCH AN ANGLE IN STANDARD POSITION IF TERMINAL ARM PASSES THROUGH  A POINT

Example 1 :

Sketch an angle in standard position so that the terminal arm passes through each point.

(a) (2, 6)

Solution : 

First let us plot the point (2, 6) in the graph paper.

(b) (-4, 2)

(c) (-5, -2) 

(d) (-1, 0)

Example 2 :

Determine the exact values of the sine, cosine, and tangent ratios for each angle

Solution :

By drawing a perpendicular line from A, we get a triangle OAB.

In triangle OAB,

OA  =  Hypotenuse side

OB  =  Adjacent side and AB = Opposite side

Since the terminal arm lies in first quadrant, we have to take positive sign for sin 60.

(ii)  

By drawing a perpendicular line from A, we get a triangle OAB.

In triangle OAB,

<BOA  =  180 +  θ  

180 +  θ  = 225

 θ  =  225 - 180  =  45

Since the terminal arm lies in the 3rd quadrant, we have to use positive sign for tan and cot only.

(iii)

By drawing a perpendicular line from A, we get a triangle OAB.

In triangle OAB,

<AOB  =  180 - θ  

<AOB  =  180 - 150  

<AOB  =  30

(iv)

Example 3 :

The coordinates of a point P on the terminal arm of each angle are shown. Write the exact trigonometric ratios sin θ, cos θ, and tan θ for each.

Solution :

Since the terminal arm lies in 3rd quadrant, we have to take positive signs for all trigonometric ratios.

(ii)

Since the terminal arm lies in 3rd quadrant, we have to take positive sign only for tan and cot.

(iii)

Since the terminal arm lies in 4th quadrant, we have to take positive sign only for cos and sec.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.