What is tan(arccos3/4)
Consider a right triangle with sides of a = 3, b = sqrt7 and a hypotenuse of c = 4.
Note that the side lengths satisfy the Pythagorean theorem: a^2 + b^2 = c^2
Consider the angle B of that triangle with cosine 3/4
The tangent of B is b/a = (sqrt7)/3 = 0.88192
To find the value of tan(arccos(3/4)), we can follow these steps:
Step 1: Determine the angle whose cosine is 3/4.
The arccosine (or inverse cosine) function considers the ratio of adjacent side to hypotenuse in a right-angled triangle. In this case, the adjacent side is 3 and the hypotenuse is 4.
We can use the Pythagorean theorem to find the remaining side:
Opposite side = sqrt(hypotenuse^2 - adjacent side^2)
= sqrt(4^2 - 3^2)
= sqrt(16 - 9)
= sqrt(7)
So, the opposite side is sqrt(7). Hence, we have a right-angled triangle with an adjacent side of 3, opposite side of sqrt(7), and a hypotenuse of 4.
Step 2: Determine the value of tangent for the angle.
Tangent is defined as the ratio of opposite side to adjacent side in a right-angled triangle.
In our case, the opposite side is sqrt(7) and the adjacent side is 3.
So, tangent(theta) = opposite side / adjacent side
= sqrt(7) / 3
Therefore, tan(arccos(3/4)) = sqrt(7) / 3.