Question

Suppose an arc of length s lies on the unit circle x² + y² = 1, starting at the point (1,0) and terminating at the point (x,y). Use a calculator to find the approximate coordinates for (x,y). (Hint: x = cos s and y = sin s.) S - 1.7 (x,y) = 0 (Type an ordered pair. Round to four decimal places as needed.)

Answer 1

To find the coordinates of a point on the unit circle given arc length s = 1.7, calculate cos(s) for x and sin(s) for y using a calculator. The approximate coordinates are (-0.1288, 0.9917) when rounded to four decimal places.

Step-by-step explanation:

The question is asking to find the coordinates (x, y) of a point on the unit circle where arc length s is given as 1.7. In this scenario, we can utilize the unit circle's fundamental properties, where x equals cosine of s (cos(s)) and y equals sine of s (sin(s)). Since the radius of the unit circle is 1, the arc length s is equivalent to the angle in radians. Hence, to find the coordinates, calculate cos(1.7) and sin(1.7), using a calculator and rounding off to four decimal places.

Using a calculator, we find:

• x = cos(1.7) ≈ -0.1288
• y = sin(1.7) ≈ 0.9917

Therefore, the approximate coordinates of the point on the unit circle are (-0.1288, 0.9917).