Solve the given triginometric equation analytically. Use values of x for 0 less than or equal to x less than 2pi
P.S Thanks Reiny for your last post, if you are still online.
what equation?
Oops sorry the equation is:
tan x + 1 = 0
P.S Please stay online I have a test tommorow and I really need your amazing help on this stuff :)
I hope you know the CAST rule, telling you were each of the trig functions is either + or -
tanx + 1 = 0
tanx = -1 so the angle x must be in II or IV
the angle in standard position is 45º,
some call it the related acute angle.
in II x must be 180+45 = 135
in IV x must be 360-45 = 315
you should always check your answers with your calculor.
e.g. tan 315 = -1, does that work in our equation ??
To solve a trigonometric equation analytically, we need to find the values of x that satisfy the equation within the given interval.
Since you mentioned the interval 0 ≤ x < 2π, we know that we are looking for solutions within one full cycle of the trigonometric functions.
Now, you haven't provided the specific trigonometric equation, so let's consider a general example:
sin(x) = 0
To solve this equation, we need to recall the solutions of sin(x) = 0. This occurs when the angle x is a multiple of π (pi):
x = nπ, where n is an integer.
Since you mentioned the interval 0 ≤ x < 2π, we need to find values of n that satisfy this condition. Here are the possible values for n:
n = 0: x = 0π = 0
n = 1: x = 1π = π
Therefore, the solutions within the given interval are x = 0 and x = π.
Note that there could be other equations with different trigonometric functions or additional terms, and the approach to solve them analytically may vary.