FINDING TRIG FUNCTIONS IF THE TERMINAL SIDE PASSES THROUGH GIVEN POINT

Finding Trig Functions if the Terminal Side Passes Through Given Point

Here we are going to see finding trig functions if the terminal side passes through given point.

Finding Trig Functions if the Terminal Side Passes Through given Point - Examples

Question 1 :

Determine the exact values of sin θ, cos θ and tan θ if the terminal arm of an angle in standard position passes through the given point.

a) P (-5, 12)

Solution :

Horizontal distance  =  5, vertical distance  =  12

Length of hypotenuse side  =  √12² + 5²

  =  √(144 + 25)

  =  √169   

  =  13

Since the terminal arm lies in second quadrant, we have to use positive sign for sin and cosec.

sin θ  =  12/13, cos θ  =  -5/13 and tan θ  =  -12/5

(b) P(5, -3)

Solution :

Horizontal distance  =  5, vertical distance  =  3

Length of hypotenuse side  =  √5² + 3²

  =  √(25 + 9)

  =  √34   

Since the terminal arm lies in fourth quadrant, we have to use positive sign for cos and sec.

sin θ  =  -5/√34, cos θ  =  3/√34 tan θ  =  -5/3

(c) P(6, 3)

Solution :

Horizontal distance  =  6, vertical distance  =  3

Length of hypotenuse side  =  √6² + 3²

  =  √(36 + 9)

  =  √45  =  3√5

Since the terminal arm lies in first quadrant, we have to use positive sign for all trigonometric ratios.

sin θ  =  3/3√5  =  1/√5

cos θ  =  6/3√5  =  2/√5

 tan θ  =  1/2

d) P(-24, -10)

Solution :

Horizontal distance  =  24, vertical distance  =  10

Length of hypotenuse side  =  √24² + 10²

  =  √(576 + 100)

  =  √676  =  26

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

sin θ  =  -10/26  =  -5/13

cos θ  =  -24/26  =  -12/13

 tan θ  =  5/12

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