Find sin A, tg A and ctg And if for an acute angle A cos A = 0.8

According to the basic trigonometry formulas sin²А + cos²А = 1.

To find the sine from this formula, we express it in terms of the cosine:

sin²А = 1 – cos²А;

sin А = √ (1 – cos²А).

Substitute the known value for the cosine:

sin A = √ (1 – (0.8) ²) = √ (1 – (4/5) ²) = √ ((5² – 4²) / 5²) = √ ((25 – 16) / 5²) = √ (9 / 5²) = 3/5.

Let us now find the tangent of angle A. According to the basic formulas of trigonometry, this is the ratio of the sine of a given angle to the cosine:

tg A = sin A / cos A = (3/5) / (4/5) = 3/4.

Since ctg A = 1 / tg A, then

ctg A = 1 / (3/4) = 4/3.