Answer: The new point might be is 47,8 by applying the rule to both x and y
Step-by-step explanation:
Answer:
1,020seconds
Step-by-step explanation:
If Kristen gets home by 5:34pm and dinner is ready by 5:51pm, dorat we need to know interval of time between when when Kristen got home and the dinner time. Since the difference is within minutes, the distance will be the difference between the minutes hand .e 51-34 which is 17minutes.
To get the amount of seconds within this period, we will have to convert 17mimutes to seconds.
1minutes = 60seconds
17minutes = x seconds
Cross multiplying
x = 17×60
x = 1020seconds
Answer:
Can you put a picture of the table? I don’t know how to do the math if you don’t show the table
Step-by-step explanation:
Recall the Pythagorean identity,
![\sin^2(\theta) + \cos^2(\theta) = 1](https://tex.z-dn.net/?f=%5Csin%5E2%28%5Ctheta%29%20%2B%20%5Ccos%5E2%28%5Ctheta%29%20%3D%201)
Since
belongs to Q3, we know both
and
are negative. Then
![\cos(\theta) = -\sqrt{1 - \sin^2(\theta)} = -\dfrac7{25}](https://tex.z-dn.net/?f=%5Ccos%28%5Ctheta%29%20%3D%20-%5Csqrt%7B1%20-%20%5Csin%5E2%28%5Ctheta%29%7D%20%3D%20-%5Cdfrac7%7B25%7D)
Recall the half-angle identities for sine and cosine,
![\sin^2\left(\dfrac\theta2\right) = \dfrac{1 - \cos(\theta)}2](https://tex.z-dn.net/?f=%5Csin%5E2%5Cleft%28%5Cdfrac%5Ctheta2%5Cright%29%20%3D%20%5Cdfrac%7B1%20-%20%5Ccos%28%5Ctheta%29%7D2)
![\cos^2\left(\dfrac\theta2\right) = \dfrac{1 + \cos(\theta)}2](https://tex.z-dn.net/?f=%5Ccos%5E2%5Cleft%28%5Cdfrac%5Ctheta2%5Cright%29%20%3D%20%5Cdfrac%7B1%20%2B%20%5Ccos%28%5Ctheta%29%7D2)
Then by definition of tangent,
![\tan^2\left(\dfrac\theta2\right) = \dfrac{\sin^2\left(\frac\theta2\right)}{\cos^2\left(\frac\theta2\right)} = \dfrac{1 - \cos(\theta)}{1 + \cos(\theta)}](https://tex.z-dn.net/?f=%5Ctan%5E2%5Cleft%28%5Cdfrac%5Ctheta2%5Cright%29%20%3D%20%5Cdfrac%7B%5Csin%5E2%5Cleft%28%5Cfrac%5Ctheta2%5Cright%29%7D%7B%5Ccos%5E2%5Cleft%28%5Cfrac%5Ctheta2%5Cright%29%7D%20%3D%20%5Cdfrac%7B1%20-%20%5Ccos%28%5Ctheta%29%7D%7B1%20%2B%20%5Ccos%28%5Ctheta%29%7D)
belonging to Q3 means
, or
, so that the half-angle belongs to Q2. Then
is positive and
is negative, so
is negative.
It follows that
![\tan\left(\dfrac\theta2\right) = -\sqrt{\dfrac{1 - \cos(\theta)}{1 + \cos(\theta)}} = \boxed{-\dfrac43}](https://tex.z-dn.net/?f=%5Ctan%5Cleft%28%5Cdfrac%5Ctheta2%5Cright%29%20%3D%20-%5Csqrt%7B%5Cdfrac%7B1%20-%20%5Ccos%28%5Ctheta%29%7D%7B1%20%2B%20%5Ccos%28%5Ctheta%29%7D%7D%20%3D%20%5Cboxed%7B-%5Cdfrac43%7D)