We can see here that the terminal point is 3.42 radius lengths (approximately ) to the right of the circle's vertical diameter.
We see here that in order for us to find the position of the terminal point, we will need to calculate the arc length that actually corresponds to the given angle and then convert it into radius lengths.
The following are given as thus:
- Angle measurement: 2.1 radians
Therefore, to calculate the arc length, we use the formula:
Arc length = Angle measurement × Circle radius
Arc length = 2.1 × 3 = 6.3 cm
Circle's radius = 3 cm
The vertical diameter has a length of 6 cm (2 × 3 cm).
Thus, in order to find the number of radius lengths to the right of the vertical diameter, we divide the arc length by the length of the vertical diameter:
We have:
Number of radius lengths = Arc length / Vertical diameter length
Number of radius lengths = 6.3 cm / 6 cm ≈ 1.05
The terminal point = 1.05 radius lengths to the right of the circle's vertical diameter.
Terminal point position = Number of radius lengths × Circle radius
Terminal point position = 1.05 * 3 cm ≈ 3.15 cm
Hence, the terminal point is approximately 3.15 cm to the right of the circle's vertical diameter.
The terminal point = 3.42 radius lengths to the right of the circle's vertical diameter, which corresponds to approximately 3.15 cm in distance from the circle's center.
The complete question is:
An angle measures 2.1 radians and its initial ray points in the 3 -o'clock direction. a circle with a radius 3 cm long is centered at the angle's vertex. the terminal point is how many radius lengths to the right of the circle's vertical diameter?