Final answer:
Angle a can be found using the inverse cosine function on a calculator, which gives the principal value for cos-1(0.8290). This angle will be less than 90° because the cosine is positive and decreases as the angle increases from 0°.
Step-by-step explanation:
To find the angle a when cos a is given as 0.8290, one can use the inverse cosine function, often represented on calculators and in mathematics software as acos or cos-1. The inverse cosine function returns the angle whose cosine is the specified value. The angle a is thus calculated as cos-1(0.8290).
By using a calculator, the approximate value of angle a can be determined. Remember that the result will be in degrees if the calculator is set to degree mode, which is common in most high school level problems. Since the cosine function is periodic, an infinite number of angles will have the same cosine value, but for practical purposes, we typically consider the principle value which is the angle between 0° and 180°.
As an additional point of reference, since cos 0 = 1, as the angle grows from 0, the cosine value decreases from 1 towards -1, reaching -1 at 180°. Therefore, an angle with a cosine value of 0.8290 would be less than 90°.