Final answer:
In trigonometry, we can find the exact values of the six trigonometric functions for a point on the terminal side of an angle in standard position. The values of these functions can be found using the coordinates of the corresponding point on the unit circle and the ratios of the sides of a right triangle formed on the unit circle. The six trigonometric functions are sine, cosine, tangent, cosecant, secant, and cotangent.
Step-by-step explanation:
In trigonometry, given a point on the terminal side of θ in standard position, we can determine the exact values of the six trigonometric functions for that point. The six trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).
To find the exact values of these functions, we first need to determine the coordinates of the point on the unit circle that corresponds to the reference angle of θ. The x-coordinate of this point represents the cosine (cos θ) and the y-coordinate represents the sine (sin θ).
Using these coordinates, we can then find the values of the other trigonometric functions by taking the ratios of the sides of the right triangle formed on the unit circle. For example, the tangent of θ (tan θ) is equal to the sine of θ divided by the cosine of θ (sin θ / cos θ).