Question

Найти sin a, если cos a=-(5/13)

Answer 1

$Sin \alpha = \sqrt{1 - Cos ^{2} \alpha } = \sqrt{1-(- \frac{5}{13}) ^{2} } = \sqrt{1- \frac{25}{169} }= \sqrt{ \frac{144}{169} } = \frac{12}{13}$

Answer 2

To find the value of sin(a) given that cos(a) = -5/13, we can use the Pythagorean trigonometric identity, which states:

sin^2(a) + cos^2(a) = 1.

Since we know cos(a) = -5/13, we can substitute this value into the identity:

sin^2(a) + (-5/13)^2 = 1.

Now, we can solve for sin(a):

sin^2(a) + 25/169 = 1, sin^2(a) = 1 - 25/169, sin^2(a) = 144/169.

Taking the square root of both sides, we get:

sin(a) = ±√(144/169).

Now, we can simplify this further:

sin(a) = ±(12/13).

So, the possible values of sin(a) are +12/13 and -12/13, depending on the quadrant in which angle a lies. The negative sign indicates that the angle is in the third or fourth quadrant, while the positive sign indicates that the angle is in the first or second quadrant. Without additional information about the quadrant, we cannot determine the exact value of sin(a).