Using the concept of the unit circle, find the sine and tangent of the following: (a) 1305∘ Explain
Answers
Answer:
Recall that dividing a circle into 360 parts creates the degree measurement. This is an arbitrary measurement, and we may choose other ways to divide a circle. To find another unit, think of the process of drawing a circle. Imagine that you stop before the circle is completed. The portion that you drew is referred to as an arc. An arc may be a portion of a full circle, a full circle, or more than a full circle, represented by more than one full rotation. The length of the arc around an entire circle is called the circumference of that circle.
The circumference of a circle is
C
=
2
π
r
If we divide both sides of this equation by
r
, we create the ratio of the circumference, which is always
2
π
to the radius, regardless of the length of the radius. So the circumference of any circle is
2
π
≈
6.28
times the length of the radius. That means that if we took a string as long as the radius and used it to measure consecutive lengths around the circumference, there would be room for six full string-lengths and a little more than a quarter of a seventh, as shown in the diagram below.
Step-by-step explanation: