Question

HOW DO YOU FIND THE SINE, COSINE, AND TANGENT VALUES GIVEN A POINT ON A CIRCLE? BE ABLE TO PROVIDE AN EXAMPLE.

Answer 1

Answer with explanation:

Suppose a point (a,b) lies on the circle.

To find Sine, Cosine and Tangent values we need to construct a right angled triangle.

So, to Construct a right triangle inside a Circle

Draw a diameter of the circle.Join the end points of diameter to the point lying on the circle.

Angle in a Semicircle is right triangle.

So, Right triangle is constructed.The two sides can be calculated , if end points of diameter is Known and also the hypotenuse which is Diameter of the circle.

Then we can be Evaluate Sine, Cosine and Tangent values.

Answer 2

Answer: If the point of the circle P has coordinates: P=(x,y)
sine (Angle) = y/r
cosine (Angle) = x/r
tangent (Angle) = y/xw
where r=sqrt(x^2+y^2) is the radius of the circle

Example:
P=(3,4)=(x,y); x=3 and y=4
Radius of the circle: r
r=sqrt(x^2+y^2)
r=sqrt(3^2+4^2)
r=sqrt(9+16)
r=sqrt(25)
r=5

sin(Angle)=y/r
sin(Angle)=4/5

cosine(Angle)=x/r
cosine(Angle)=3/5

tangent(Angle)=y/x
tangle(Angle)=4/3