Question

16) For what number(s) x, 0 sx ST, does tan x = 1?

Answer 1

| 16 If tanx=1, then sinx= cosx. we know this is true for x= I as a base case. Sina - Cost Now, the tangent function is periodic with it's period P=nt, where n is an integea- So that, tanx - ton (x+nt). tanx=1 is, as tana= tan (at na = 1 The first positive value xo for which as stated before I. tanxo = tan (not nx) = 1 tan (7 + n) = tan (En + + which means tanx=1, if and only if x is a of the foom Entida. xe { bn , ne z only o osx = K tanx=1 is, at when, x = 7 in that intera

14). The cotx is the function undefined whenever x= 220 and x = 1+2 TM where n is an integer we start by cwriting for) as f) = Cosme Since a is undefined for each and every value of a. we want to find the points were sinx=0. Sinx. sine o x= arc Sin (o) x=0, T. Since trig functions are periodic, that's to say they go to infinity in both directions, we want to find a general foom Solution, the period of Sinx is at hence, x=2th and T+2an, where n is an integer Sinx =0 when x = 0, T, 2T, in (ocxzan) when cotx is undefined when sinx=0 at x=0, 7 and 27 in the interval ocneat

| 16 If tanx=1, then sinx= cosx. we know this is true for x= I as a base case. Sina - Cost Now, the tangent function is periodic with it's period P=nt, where n is an integea- So that, tanx - ton (x+nt). tanx=1 is, as tana= tan (at na = 1 The first positive value xo for which as stated before I. tanxo = tan (not nx) = 1 tan (7 + n) = tan (En + + which means tanx=1, if and only if x is a of the foom Entida. xe { bn , ne z only o osx = K tanx=1 is, at when, x = 7 in that intera

14). The cotx is the function undefined whenever x= 220 and x = 1+2 TM where n is an integer we start by cwriting for) as f) = Cosme Since a is undefined for each and every value of a. we want to find the points were sinx=0. Sinx. sine o x= arc Sin (o) x=0, T. Since trig functions are periodic, that's to say they go to infinity in both directions, we want to find a general foom Solution, the period of Sinx is at hence, x=2th and T+2an, where n is an integer Sinx =0 when x = 0, T, 2T, in (ocxzan) when cotx is undefined when sinx=0 at x=0, 7 and 27 in the interval ocneat