Two numbers are 15.46 and 15.48.
Use the Pythagorean theorem (a^2 + b^2 = c^2)
7^2 + 24^2 = x^2
x^2 = 625
x = 25
Given:
The point on the terminal side of theta is (4,-7).
To find:
The exact values of sin theta, secant theta, and tangent theta.
Solution:
If a point
is on the terminal side of theta and
, then
![\sin \theta=\dfrac{y}{r}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D%5Cdfrac%7By%7D%7Br%7D)
![\cos \theta=\dfrac{x}{r}](https://tex.z-dn.net/?f=%5Ccos%20%5Ctheta%3D%5Cdfrac%7Bx%7D%7Br%7D)
![\sec \theta=\dfrac{r}{x}](https://tex.z-dn.net/?f=%5Csec%20%5Ctheta%3D%5Cdfrac%7Br%7D%7Bx%7D)
![\tan \theta=\dfrac{y}{x}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%3D%5Cdfrac%7By%7D%7Bx%7D)
The point on the terminal side of theta is (4,-7). Here,
and
.
![r=\sqrt{(4)^2+(-7)^2}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%284%29%5E2%2B%28-7%29%5E2%7D)
![r=\sqrt{16+49}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B16%2B49%7D)
![r=\sqrt{65}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B65%7D)
Now,
![\sin \theta=\dfrac{-7}{\sqrt{65}}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D%5Cdfrac%7B-7%7D%7B%5Csqrt%7B65%7D%7D)
![\cos \theta=\dfrac{4}{\sqrt{65}}](https://tex.z-dn.net/?f=%5Ccos%20%5Ctheta%3D%5Cdfrac%7B4%7D%7B%5Csqrt%7B65%7D%7D)
![\sec \theta=\dfrac{\sqrt{65}}{4}](https://tex.z-dn.net/?f=%5Csec%20%5Ctheta%3D%5Cdfrac%7B%5Csqrt%7B65%7D%7D%7B4%7D)
![\tan \theta=\dfrac{-7}{4}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%3D%5Cdfrac%7B-7%7D%7B4%7D)
Therefore,
.
Answer:
is the answer
Step-by-step explanation:
Equation of the line: y = 6/5x + 1
= 5y = 6x + 5
= 6x - 5y + 5
Equation of the perpendicular line: bx - ay + k = 0
= -5x -6y + k = 0
Equation passes through (6,-6),
-5(6) -6(-6) + k = 0
-30 + 36 + k = 0
6 + k = 0
k = -6
Substituting,
-5x -6y + k = 0
-5x -6y -6 = 0
-6y = 5x + 6
(Slope-Intercept form)
Answer:
71.98
≈ 71.98175 <em>rounded to hundred-thousandths</em>