Question

If t is the distance from (1, 0) to (0.8253, 0.5646) along the circumference of the unit circle, find sin t, cos t, and tan t. (Round your answers to four decimal places if necessary.)

A) sin t ≈ 0.6, cos t ≈ 0.8, tan t ≈ 0.75
B) sin t ≈ 0.7, cos t ≈ 0.7, tan t ≈ 1.0
C) sin t ≈ 0.8, cos t ≈ 0.6, tan t ≈ 1.33
D) sin t ≈ 0.9, cos t ≈ 0.4, tan t ≈ 2.25

Answer 1

By using the coordinates (0.8253, 0.5646), which signify cos t and sin t on the unit circle, we can determine that sin t ≈ 0.5646, cos t ≈ 0.8253, and tan t ≈ 0.6841, none of which precisely match the answer choices given.

Step-by-step explanation:

To find sin t, cos t, and tan t for the distance t from (1, 0) to (0.8253, 0.5646) along the circumference of the unit circle, we can directly observe that the coordinates of the point (0.8253, 0.5646) provide the values of cos t and sin t, respectively, because a point on the unit circle at an angle t from the positive x-axis has coordinates (cos t, sin t). Therefore, cos t ≈ 0.8253 and sin t ≈ 0.5646. To find tan t, which is the ratio of sin t to cos t (tan t = sin t / cos t), we perform the division of the two obtained values. This gives us tan t ≈ 0.5646 / 0.8253, which upon calculation rounds to approximately 0.6841. Hence, the correct answer after rounding to four decimal places is sin t ≈ 0.5646, cos t ≈ 0.8253, and tan t ≈ 0.6841. This does not match any of the provided answer choices exactly, so the question may contain an error or require a different interpretation.