<span>In general, if the pyramid has 'x' sides, then it will have 'x' lateral faces. Total Number of Faces = Number of Base Faces + Number of Lateral Faces. Total Number of Faces = 2 + x. So the formula is F=x%2B2 where "x" is the number of sides that the pyramid has and "F" is the total number of faces.</span>
Answer:
![\tan(\beta)](https://tex.z-dn.net/?f=%5Ctan%28%5Cbeta%29)
Step-by-step explanation:
For many of these identities, it is helpful to convert everything to sine and cosine, see what cancels, and then work to build out to something. If you have options that you're building toward, aim toward one of them.
and ![{\sec(\theta)}={\dfrac{1}{\cos(\theta)}](https://tex.z-dn.net/?f=%7B%5Csec%28%5Ctheta%29%7D%3D%7B%5Cdfrac%7B1%7D%7B%5Ccos%28%5Ctheta%29%7D)
Recall the following reciprocal identity:
![\cot(\theta)=\dfrac{1}{\tan(\theta)}=\dfrac{1}{ \left ( \dfrac{\sin(\theta)}{\cos(\theta)} \right )} =\dfrac{\cos(\theta)}{\sin(\theta)}](https://tex.z-dn.net/?f=%5Ccot%28%5Ctheta%29%3D%5Cdfrac%7B1%7D%7B%5Ctan%28%5Ctheta%29%7D%3D%5Cdfrac%7B1%7D%7B%20%5Cleft%20%28%20%5Cdfrac%7B%5Csin%28%5Ctheta%29%7D%7B%5Ccos%28%5Ctheta%29%7D%20%5Cright%20%29%7D%20%3D%5Cdfrac%7B%5Ccos%28%5Ctheta%29%7D%7B%5Csin%28%5Ctheta%29%7D)
So, the original expression can be written in terms of only sines and cosines:
![\sin(\beta)\tan(\beta)\sec(\beta)\cot(\beta)](https://tex.z-dn.net/?f=%5Csin%28%5Cbeta%29%5Ctan%28%5Cbeta%29%5Csec%28%5Cbeta%29%5Ccot%28%5Cbeta%29)
![\sin(\beta) * \dfrac{\sin(\beta) }{\cos(\beta) } * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) } {\sin(\beta) }](https://tex.z-dn.net/?f=%5Csin%28%5Cbeta%29%20%2A%20%5Cdfrac%7B%5Csin%28%5Cbeta%29%20%7D%7B%5Ccos%28%5Cbeta%29%20%7D%20%2A%20%5Cdfrac%7B1%20%7D%7B%5Ccos%28%5Cbeta%29%20%7D%20%2A%20%5Cdfrac%7B%5Ccos%28%5Cbeta%29%20%7D%20%7B%5Csin%28%5Cbeta%29%20%7D)
![\sin(\beta) * \dfrac{\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} {\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}](https://tex.z-dn.net/?f=%5Csin%28%5Cbeta%29%20%2A%20%5Cdfrac%7B%5Csin%28%5Cbeta%29%20%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%7B---%7D%7D%7B%5Ccos%28%5Cbeta%29%20%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%7B---%7D%7D%20%2A%20%5Cdfrac%7B1%20%7D%7B%5Ccos%28%5Cbeta%29%20%7D%20%2A%20%5Cdfrac%7B%5Ccos%28%5Cbeta%29%20%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%7B---%7D%7D%20%7B%5Csin%28%5Cbeta%29%20%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%7B---%7D%7D)
![\sin(\beta) *\dfrac{1 }{\cos(\beta) }](https://tex.z-dn.net/?f=%5Csin%28%5Cbeta%29%20%2A%5Cdfrac%7B1%20%7D%7B%5Ccos%28%5Cbeta%29%20%7D)
![\dfrac{\sin(\beta)}{\cos(\beta) }](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csin%28%5Cbeta%29%7D%7B%5Ccos%28%5Cbeta%29%20%7D)
Working toward one of the answers provided, this is the tangent function.
The one caveat is that the original expression also was undefined for values of beta that caused the sine function to be zero, whereas this simplified function is only undefined for values of beta where the cosine is equal to zero. However, the questions states that we are only considering values for which the original expression is defined, so, excluding those values of beta, the original expression is equivalent to
.
Answer:
75%
Step-by-step explanation:
90/ 120 is the same as 75 or 3/4 so 75% of 120 is 90
Answer:
0.8= 2.1448=2.1379
Step-by-step explanation:
To answer this go to the guys link on top