Find cosine, tangent, cotangent and sine of 2a if sine = 0.5.

The sine of the angle is known. Let’s find its cosine, tangent, cotangent and sine of a double angle.

sin A = 0.5.

Let’s look at two cases:

1) The angle is in the first quarter, which means that the values of all the required quantities are positive.

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

0.25 + cos ^ 2A = 1;

cos ^ 2 A = 3/4;

cos A = 1/2 * 3 ^ (1/2);

tan A = sin A / cos A = 1/2 * 2 * 3 ^ (- 1/2) = 3 ^ (- 1/2);

ctg A = 3 ^ (1/2).

sin 2A = 2 * sinA * cosA = 2 * 1/2 * 1/2 * 3 ^ (1/2) = 1/2 * 3 ^ (1/2).

2) The angle is in the second quarter, all values are changed to negative.

cos A = – 1/2 * 3 ^ (1/2);

tan A = 3 ^ (- 1/2);

ctg A = 3 ^ (1/2);

sin 2A = – 1/2 * 3 ^ (1/2).