find the trig functions of angle x if the terminal side of x passes through the point (-12, 5).
the angle x is in the 2nd quadrant , hypotenuse is 13 by Pythagoras.
sinx = 5/13
cosx = -12/13
tanx = -5/12
cscx = 13/5
secx = -13/12
cotx = -12/5
To find the trigonometric functions of angle x, we need to determine the values of the sine, cosine, and tangent of x by using the coordinates of the point (-12, 5), through which the terminal side of angle x passes.
First, we need to calculate the length of the hypotenuse, the horizontal distance (adjacent side), and the vertical distance (opposite side) of the right triangle formed by the point (-12, 5) and the origin (0, 0).
The hypotenuse, denoted as r, can be found using the Pythagorean theorem:
r = √((-12)² + 5²) = √(144 + 25) = √169 = 13
The adjacent side, denoted as x, is equal to the x-coordinate of the given point (-12, 5):
x = -12
The opposite side, denoted as y, is equal to the y-coordinate of the given point (-12, 5):
y = 5
Now, we can find the trigonometric functions of angle x:
1. Sine (sin(x)):
sin(x) = y / r = 5 / 13
2. Cosine (cos(x)):
cos(x) = x / r = -12 / 13
3. Tangent (tan(x)):
tan(x) = y / x = 5 / -12
Therefore, the trigonometric functions of angle x are:
sin(x) = 5 / 13
cos(x) = -12 / 13
tan(x) = 5 / -12