Why do people like the arcane functions like sec and csc. Isn't the whole thing simply just 1/sinx=√2 so the solutions are x€{y+2kπ, π-y+2kπ|k€Z} where y=arcsin(√2/2)=π/4
@StuartSimon in my country of origin ( tanx)'=1/cos^2(X) nice and simple 1/cos^2(X)=(1+tan^2(X)) very useful especially for Weierstrass substitution I know the definition for sec and stuff just never used them
The correct values are pi/4 and 3pi/4 as shown in the graphs and in the first method presented. For some reasons, SyberMath said "5pi/4" -- just a slip of the tongue.
Definitely used the 1st method.
How is 3*PI over 4 not a solution since sine is positive in the 1st and 2nd quadrants?
Why do people like the arcane functions like sec and csc. Isn't the whole thing simply just 1/sinx=√2 so the solutions are
x€{y+2kπ, π-y+2kπ|k€Z} where y=arcsin(√2/2)=π/4
In calculus, knowing them leads to being able to solve more integrals. Secant actually shows up in a lot of identities when paired with tangent.
@StuartSimon in my country of origin ( tanx)'=1/cos^2(X) nice and simple
1/cos^2(X)=(1+tan^2(X)) very useful especially for Weierstrass substitution
I know the definition for sec and stuff just never used them
Secant and cosecant figure into cartography and navigation. For arcane trig functions check out versine and haversine and related friends.
(secx)/(tanx) = (1/cosx)/(sinx/cosx) = 1/sinx = ✓2
sinx = 1/✓2
x = π/4 + 2πn or 3π/4 + 2πn
x = 45° + 2πn or 135° + 2πn
n = 0, 1, 2, 3 ...
The correct values are pi/4 and 3pi/4 as shown in the graphs and in the first method presented. For some reasons, SyberMath said "5pi/4" -- just a slip of the tongue.
Ah, you are right! It seems I made a mistake! Thanks for pointing it out 🙂
5π/4 or 3π/4 ?
Should be 3π/4 he was thinking 1 thing and saying another. How some people would say it's a pointer error
@dan-florinchereches4892 yeah, I think so