Question

find all solutions tan^2 θ − 1 = 0

Answer 1

\(\large tan^2\theta-1=0 \)
\(\large tan^2\theta=1 \)
\(\large tan\theta=1 \) or \(\large tan\theta=-1 \)

can you solve these two equations?

Answer 2

i dont know how

Answer 3

The person before me has made it simple.
You find the value of theta for tan inverse 1 and tan inverse -1.

Answer 4

how do you do that

Answer 5

have you used the unit circle before?

Answer 6

yea

Answer 7

ok... let's just do that first equation, \(\large tan\theta=1 \)
in terms of sine and cosine, that equation can be written as \(\large \frac{sin\theta}{cos\theta}=1 \).

what angle on the unit circle gives the same value for the sin and cos ?

Answer 8

pi/4 and 3pi/4

Answer 9

pi/4 is one of 'em but 3pi/4 are opposites (it is a solution for the second equation though)
see page 3 here: http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

Answer 10

5pi/4

Answer 11

yes... so for the first equation, the solutions are pi/4, and 5pi/4

what about \(\large tan\theta=-1 \)... can you give me the solution(s) for this one?

Answer 12

3pi/4 and7pi/4

Answer 13

yes...
those are the solutions for theta from 0 to 2pi. did you want the general solution?

Answer 14

yes please

Answer 15

oops... ALL solutions... ok...

Answer 16

sorry... the solutions are multiples of pi/2 apart

Answer 17

Because ByteMe is doing his best to help, here's a medal.

Answer 18

so your general solution (all solutions) is pi/4 + n*pi/2, where n = ....-2, -1, 0, 1, 2, ...

Answer 19

thanks @CeroOscura94 ... :)

Answer 20

thank i got it :)