Question

Найдите cosa, tga, ctga, если sina 15/17?​

Answer 1

Ответ:

$cosa=\sqrt{1-sin^2a}=\sqrt{1-(\frac{15}{17} )^2} =\sqrt{1-\frac{225}{289} } =\sqrt{\frac{289-225}{289} } =\sqrt{\frac{64}{289} } =\frac{8}{17}$

$tga=\frac{sina}{cosa} =\frac{\frac{15}{17} }{\frac{8}{17} } =\frac{15}{8}$

$ctga=\frac{cosa}{sina} =\frac{\frac{8}{17} }{\frac{15}{17} } =\frac{8}{15}$

Объяснение:

Answer 2

To find the values of cos(a), tan(a), and cot(a) when sin(a) is given as 15/17, we can use the Pythagorean trigonometric identity:

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

Given sin(a) = 15/17, we can find cos(a) as follows:

sin^2(a) + cos^2(a) = 1 (15/17)^2 + cos^2(a) = 1 225/289 + cos^2(a) = 1 cos^2(a) = 1 - 225/289 cos^2(a) = 64/289

Taking the square root of both sides:

cos(a) = ± √(64/289)

Since cosine is positive in the first and fourth quadrants, we take the positive value:

cos(a) = √(64/289) = 8/17

Now, we can find tan(a) using the relationship:

tan(a) = sin(a) / cos(a) tan(a) = (15/17) / (8/17) tan(a) = 15/8

Finally, we can find cot(a) using the relationship:

cot(a) = 1 / tan(a) cot(a) = 1 / (15/8) cot(a) = 8/15

So, the values are:

cos(a) = 8/17 tan(a) = 15/8 cot(a) = 8/15