Question

Знайдіть sin a tg a якщо cos a= - п'ять тринадцятих ​

Answer 1

Найти sina и tga, если cosa=-5/13. Решение: sina=√(1-cos²a)=√(1-(-5/13)²)=√(1-25/69)=√(144/169)=±12/13; tga=(sina)/(cosa)=±12/13÷(-5/13)=±12*(-1/5)=±-12/5=± -2,4.

Примечание. a – альфа.

Answer 2

Given that cos a = -5/13

Using the Pythagorean identity for sine and cosine: sin^2 a + cos^2 a = 1 sin^2 a + (-5/13)^2 = 1 sin^2 a + 25/169 = 1 sin^2 a = 1 - 25/169 sin^2 a = 144/169 sin a = ± √(144/169)

Since sin a is positive and cos a is negative, sin a must also be negative (since they have opposite signs in the unit circle).

sin a = - √(144/169) = -12/13

Now, we can use the definition of tangent to find tg a:

tan a = sin a / cos a tg a = -12/13 / (-5/13) tg a = 12/5

Therefore, sin a = -12/13 and tg a = 12/5.