Find tan theta if theta is an angle in standard position and the point with coordinates (–12, 5) lies on the terminal side of the angle.
Your x-coordinate of the given point contains a non-readable character, is it (√12,5) ?
If so, then
tanØ = 5/√12
If it is something else, then
tanØ is simply y/x
Suppose the terminal side of an angle in standard position with measure 0 contains the point P (5,7). Find sin0 , cos0 , and tan0 . Then find the measures of the angle to the nearest degree.
To find the value of tan θ, we can use the tangent function, which is defined as the ratio of the sine of the angle to the cosine of the angle.
First, we need to determine the values of sine and cosine from the given point (-12, 5). In standard position, the x-coordinate represents the cosine value, and the y-coordinate represents the sine value.
Given: (x, y) = (-12, 5)
To find the sine value:
sin θ = y / r, where r is the distance from the origin to the point (-12, 5). Applying the Pythagorean theorem:
r = sqrt(x^2 + y^2)
r = sqrt((-12)^2 + 5^2)
r = sqrt(144 + 25)
r = sqrt(169)
r = 13
sin θ = y / r
sin θ = 5 / 13
To find the cosine value:
cos θ = x / r
cos θ = -12 / 13
Now that we have the values for sine and cosine, we can find the tangent value:
tan θ = sin θ / cos θ
tan θ = (5 / 13) / (-12 / 13)
tan θ = 5 / (-12)
tan θ = -5/12
Therefore, the value of tan θ is -5/12.