Question

Use trigonometric identities and algebraic methods, as necessary, to solve the following trigonometric equation. Please identify all possible solutions by including allanswers in [0, x) and indicating the remaining answers by using n to represent any integer. Round your answer to four decimal places, if necessary. If there is no solution,indicate "No Solution."Stan(x) + 5 = 0

Answer 1

we have the equation

`\begin{gathered} 5\tan x+5=0 \\ 5\tan x=-5 \\ \tan x=-(5)/(5) \\ \tan x=-1 \end{gathered}`

Remember that

tanx=1 -----> for x=45 degrees--------> x=pi/4

the value of the tangent is negative in the II quadrant and In the IV quadrant

In this problem

the domain for x is the interval [0,pi)

so

the quadrant of the solution is the second

the angle x is equal to

pi-pi/4=3pi/4

the solution for x=3pi/4