Angle θ is an acute angle of a right triangle. Determine the value of cot θ given the value of sin θ below. what is sin 15/17?
To determine the value of cot θ, we need to find the value of cos θ.
Since θ is an acute angle of a right triangle, we can use the Pythagorean theorem to find the value of cos θ.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, let the length of the side opposite θ be 15 and the length of the hypotenuse be 17.
Using the Pythagorean theorem, we can find the length of the adjacent side:
17^2 = 15^2 + Adjacent Side^2
289 = 225 + Adjacent Side^2
Adjacent Side^2 = 289 - 225 = 64
Adjacent Side = √64 = 8
Now, we can find the value of cos θ by dividing the length of the adjacent side by the length of the hypotenuse:
cos θ = Adjacent Side / Hypotenuse = 8 / 17
Finally, we can find the value of cot θ by taking the reciprocal of the value of tan θ, which is equal to sin θ / cos θ:
cot θ = cos θ / sin θ = 8 / 15.
Hence, cot θ = 8/15.
To determine the value of cot θ given the value of sin θ, we need to use the relationship between the trigonometric functions.
In a right triangle, cot θ is equal to the adjacent side divided by the opposite side:
cot θ = adjacent side / opposite side
To find cot θ, we need to know the values of the adjacent side and the opposite side.
Given sin θ = 15/17, we can use the Pythagorean identity to find the value of the third side, which is the hypotenuse of the right triangle.
Let's label the sides of the right triangle:
Opposite side = 15
Adjacent side = x (unknown)
Hypotenuse = 17
Using the Pythagorean identity (a^2 + b^2 = c^2), we can solve for x:
x^2 + 15^2 = 17^2
x^2 + 225 = 289
x^2 = 289 - 225
x^2 = 64
x = √(64)
x = 8
Now we can find cot θ using the values we have:
cot θ = adjacent side / opposite side
cot θ = x / 15
cot θ = 8 / 15
Therefore, the value of cot θ is 8/15.