I need to see the angles to answer this question
Answer:
−π
----
4
Step-by-step explanation:
Alright, archtan /
tan
−
1
(
x
)
is the inverse of tangent. Tan is
sin
cos
. Like the inverse of sin, the inverse of tan is also restricted to quadrants 1 and 4.
Knowing this we are solving for the inverse of tan -1. We are basically being asked the question what angle/radian does tan(-1) equal. Using the unit circle we can see that tan(1)= pi/4.
Since the "Odds and Evens Identity" states that tan(-x) = -tan(x). Tan(-1)= -pi/4.
Knowing that tan is negative in quadrants 2 and 4. the answer is in either of those two quadrants. BUT!!! since inverse of tan is restricted to quadrants 1 and 4 we are left with the only answer -pi/4.
![\bf \sqrt{n}< \sqrt{2n+5}\implies \stackrel{\textit{squaring both sides}}{n< 2n+5}\implies 0\leqslant 2n - n + 5 \\\\\\ 0 < n+5\implies \boxed{-5 < n} \\\\\\ \stackrel{-5\leqslant n < 2}{\boxed{-5}\rule[0.35em]{10em}{0.25pt}0\rule[0.35em]{3em}{0.25pt}2}](https://tex.z-dn.net/?f=%5Cbf%20%5Csqrt%7Bn%7D%3C%20%5Csqrt%7B2n%2B5%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bsquaring%20both%20sides%7D%7D%7Bn%3C%202n%2B5%7D%5Cimplies%200%5Cleqslant%202n%20-%20n%20%2B%205%20%5C%5C%5C%5C%5C%5C%200%20%3C%20n%2B5%5Cimplies%20%5Cboxed%7B-5%20%3C%20n%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B-5%5Cleqslant%20n%20%3C%202%7D%7B%5Cboxed%7B-5%7D%5Crule%5B0.35em%5D%7B10em%7D%7B0.25pt%7D0%5Crule%5B0.35em%5D%7B3em%7D%7B0.25pt%7D2%7D)
namely, -5, -4, -3, -2, -1, 0, 1. Excluding "2" because n < 2.
Just put them in order from least to greatest and find out in between which number to put them . For example put 24 between 20 and 25.
Hope that helps .
If the discriminant of a quadratic equation, given by B^2-4AC is positive, it has 2 real solutions. If 0, it has 1 real solution and if negative it has 0 real solutions.
