Question 552037
Angles are often represented with Greek letters.
The Greek letter theta looks like this {{{theta}}}.
Half a century ago, we used to look up values for sine and cosine in trigonometric tables. (We also looked up logarithms in tables. There were no calculators back then). I have not looked at a trigonometric table for a long time. Your table may be different from the ones I have seen. The one I used back then would have angle measurements in degrees on a column on the left, with (additional) fractions of a degree as headings on a line at the top. On the right hand side we had a column with the measure of the complementary angle in degrees (with additional fractions on a line at the bottom. The numbers in the middle of the table were sine of the angle read at left and cosine of the supplementary angle read at right.
I could not find my old table, but I have an abbreviated one. It tells me that
(a) {{{sin(26.1degrees)=0.4400}}} 
(b) It also says that {{{cos(36.06degrees)}}} is about 0.8084.
So if {{{cos(theta)=0.8084}}}, {{{theta=36.1degrees}}} (to the nearest tenth of a degree). Because trigonometric functions are periodic, and {{{cos(theta)= cos(-theta)}}}, there are infinity of other angles with the same cosine, like -36.1 degrees, (-36.1+360) degrees, (-36.1+720) degrees, and so on, as well as (36.1+360) degrees, (36.1+720) degrees, and so on. However, the only acute angle {{{theta}}} with {{{cos(theta)=0.8084}}} is 36.1 degrees.