How Do You Calculate Sine from a Point on an Angle's Terminal Side?

[danglade]

urgent: sines

if you are given a point on the terminal side of an angle 0 , explain how to find sin 0

Please i really need help with this one

 

[Gib Z]

Sorry but I don't understand your question :( If you want to know what the value of sin 0 is, have you seen the trigonometric functions defined on the unit circle?

 

[danglade]

thats why, because my teacher gave me that question in the review and i don't understand either

 

[Gib Z]

Ok don't worry about the unit circle. Draw a right angled triangle, with one of the smaller angles being T degrees. Name the opposite side X, hypotenuse Y and the adjacent side Z. Now think in your head about changing the angle T. As T gets smaller, so does the Side X, and the Side Y. But Y only gets smaller by a tiny amount, in fact the smallest reducing the angle can make it is the length of side Z. Side X doesn't stay a finite amount though, it becomes zero when you make the angle zero. Hence the Sine of T is 0/Z is if is 0. ie sin 0= 0.

 

[rohanprabhu]

@GibZ: Which point does "a point on the terminal side of an angle 0" refer to??

 

[HallsofIvy]

thats why, because my teacher gave me that question in the review and i don't understand either

NO, your teacher did NOT give you that question! You teacher would expect you to know immediately that sin 0= 0! You teacher probably asked about sin(\theta).

 

[HallsofIvy]

If you are given a point on the terminal side of an angle of measure, \theta, set up a coordinate system so that the vertex of the angle is at (0,0), the initial side of the angle is along the positive x-axis and the distance from one to the given point on the terminal side is 1. Then sin(\theta)= y coordinate of the point.

Alternatively, drop a perpendicular from the given point on the terminal side to the initial side. Measure N, the distance from the vertex of the angle to the foot of the perpendicular, and H, the distance from the vertex to the given point. sin(\theta) = N/H.