Final answer:
To find sin t, cos t, and tan t along the circumference of the unit circle, use the coordinates (0.6967, 0.7174) to calculate the angle t and then find the respective trigonometric values: sin t is 0.7174, cost is 0.6967, and tan t is the ratio of sin t to cos t.
Step-by-step explanation:
To find sin t, cos t, and tan t for the distance t from the point (1, 0) to the point (0.6967, 0.7174) on the unit circle, we first recognize that these two points represent two positions on the unit circle. Since we're given cartesian coordinates, to compute the trigonometric functions, we need to determine the angle that corresponds to the point (0.6967, 0.7174).
The angle t can be found using the inverse tangent function since the tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Hence, t = tan-1(0.7174 / 0.6967). After finding the angle t, the sine, cosine, and tangent values can be calculated using their respective trigonometric definitions.
Sine is defined as the ratio of the opposite side over the hypotenuse, which in the unit circle corresponds to the y-coordinate. Therefore, sin t = 0.7174. Similarly, cosine is the ratio of the adjacent side over the hypotenuse, corresponding to the x-coordinate, so cos t = 0.6967. Lastly, the tangent of the angle is the ratio of sine over cosine, hence tan t = sin t / cos t.