The sine of the angle is 0.4. What is the tangent of this angle?

We know from the condition that the sine of a certain angle is equal to 0.4. And you need to find what the tangent of the same angle is equal to.

Let’s start by remembering that tangent can be written as the ratio of sine to cosine of the same angle.

We get:

tg a = sin a / cos a;

We need to find cos a.

To do this, we will apply the basic trigonometric identity:

cos ^ 2 a + sin ^ 2 a = 1;

cos ^ 2 a = 1 – sin ^ 2 a.

Substitute values and perform calculations:

cos ^ 2 a = 1 – 0.16 = 0.84;

cos a = √0.84 = 2√21 / 10 = √21 / 5.

tg a = 0.4: √21 / 5 = 2√21 / 21.