Question

1)найти косинус острого угла,если его синус равен 12\13 2)найти тангенс острого угла, если его синус равен 12\13

Answer 1

1)найти косинус острого угла,если его синус равен 12\13
cos^2 = 1 - sin^2  = 1 - (12/13)^2 =25/169
cos =  5/13

2)найти тангенс острого угла, если его синус равен 12\13

cos =  5/13
tg = sin/cos = 12/13  /  5/13 = 12/5

Answer 2

1)найти косинус острого угла,если его синус равен 12\13
принадлежит 1 четверти косинус положителен
cos²=1-(12/13)²=25/169
cos=5/13
2)найти тангенс острого угла, если его синус равен 12\13
угол принадлежит первой четверти синус косинус тангенс больше 0
tg=sin/cos=12/13/(√1-(12/13)²)=12/13 : 5/13=12/5

Answer 3

Finding the cosine of an acute angle with a given sine

To find the cosine of an acute angle when its sine is given, we can use the Pythagorean identity, which states that for any angle in a right triangle, the square of the sine plus the square of the cosine equals 1.

Let's denote the given sine as sin(x) and the unknown cosine as cos(x). According to the Pythagorean identity, we have:

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

Since we know that sin(x) = 12/13, we can substitute this value into the equation:

(12/13)^2 + cos^2(x) = 1

Simplifying the equation, we have:

144/169 + cos^2(x) = 1

Subtracting 144/169 from both sides, we get:

cos^2(x) = 1 - 144/169

Taking the square root of both sides, we find:

cos(x) = ±√(1 - 144/169)

Since we are dealing with an acute angle, the cosine value will be positive. Therefore, we have:

cos(x) = √(1 - 144/169)

To calculate the value of cos(x), we can substitute the given values into the equation and evaluate it.

Let's calculate the value of cos(x) using the given information.

cos(x) = √(1 - 144/169) = √(169/169 - 144/169) = √(25/169) = 5/13

Therefore, the cosine of the acute angle is 5/13.