9^4 + 3^3
= 9•9•9•9 + 3•3•3
= 6,561 + 27
= 6,588
Answer:
![\bold{cot(t) =\dfrac{12}{5}}](https://tex.z-dn.net/?f=%5Cbold%7Bcot%28t%29%20%3D%5Cdfrac%7B12%7D%7B5%7D%7D)
Step-by-step explanation:
Given that:
![Cosec (t) = -\frac{13}5](https://tex.z-dn.net/?f=Cosec%20%28t%29%20%3D%20-%5Cfrac%7B13%7D5)
for ![\pi < t < \frac{3 \pi}2](https://tex.z-dn.net/?f=%5Cpi%20%3C%20t%20%3C%20%5Cfrac%7B3%20%5Cpi%7D2)
That means, angle
is in the 3rd quadrant.
To find:
Value of cot(t)
Solution:
First of all, let us recall what trigonometric ratios are positive and what trigonometric ratios are negative in 3rd quadrant.
In 3rd quadrant, tangent and cotangent are positive.
All other trigonometric ratios are negative.
Let us have a look at the following identity:
![cosec^2\theta -cot^2\theta =1](https://tex.z-dn.net/?f=cosec%5E2%5Ctheta%20-cot%5E2%5Ctheta%20%3D1)
here, ![\theta =t](https://tex.z-dn.net/?f=%5Ctheta%20%3Dt)
So, ![cosec^2t-cot^2t=1](https://tex.z-dn.net/?f=cosec%5E2t-cot%5E2t%3D1)
![\Rightarrow (-\dfrac{13}{5})^2-cot^2t=1\\\Rightarrow (\dfrac{169}{25})-cot^2t=1\\\Rightarrow \dfrac{169}{25}-1=cot^2t\\\Rightarrow \dfrac{169-25}{25}=cot^2t\\\Rightarrow \dfrac{144}{25}=cot^2t\\\Rightarrow cot(t)=\pm\sqrt{\dfrac{144}{25}}\\\Rightarrow cot(t)=\pm\dfrac{12}{5}](https://tex.z-dn.net/?f=%5CRightarrow%20%28-%5Cdfrac%7B13%7D%7B5%7D%29%5E2-cot%5E2t%3D1%5C%5C%5CRightarrow%20%28%5Cdfrac%7B169%7D%7B25%7D%29-cot%5E2t%3D1%5C%5C%5CRightarrow%20%5Cdfrac%7B169%7D%7B25%7D-1%3Dcot%5E2t%5C%5C%5CRightarrow%20%5Cdfrac%7B169-25%7D%7B25%7D%3Dcot%5E2t%5C%5C%5CRightarrow%20%5Cdfrac%7B144%7D%7B25%7D%3Dcot%5E2t%5C%5C%5CRightarrow%20cot%28t%29%3D%5Cpm%5Csqrt%7B%5Cdfrac%7B144%7D%7B25%7D%7D%5C%5C%5CRightarrow%20cot%28t%29%3D%5Cpm%5Cdfrac%7B12%7D%7B5%7D)
But, angle
is in 3rd quadrant, so value of
![\bold{cot(t) =\dfrac{12}{5}}](https://tex.z-dn.net/?f=%5Cbold%7Bcot%28t%29%20%3D%5Cdfrac%7B12%7D%7B5%7D%7D)
Answer:
C.
Step-by-step explanation:
-3 7/8 rounds down to -4
4.63 rounds up to 5
-4 x 6 + 5
-24 + 5
-19
her answer (-19.14) also rounds to -19
So yes, it is reasonable and the correct response is C.
True? I dont know what you're trying to ask. if you're asking whether or not it's true, it is.