Question

Any help you could give me with this problem would be grand!

tan theta=-1

I already found the equation that expresses the value of theta in terms of an appropriate inverse trigonometric expression: theta=tan^-1(-1)

But I need help answering: on the inverval [0, 2pi], what values of theta satisfy that equation?

Would it be 3pi/4 and -pi/4.

Also, how would you write an expression for all solutions to the equation?

Answer 1

since tangent it periodic with period \(\pi\) youcoud say
\[\frac{3\pi}{4}+k\pi\] for \(k\in \mathbb{Z}\)

Answer 2

But I need help answering: on the inverval [0, 2pi],

Would it be 3pi/4 and -pi/4.

NO

Answer 3

because \(-\frac{\pi}{4}\) is not in the interval \([0,2\pi)\)

Answer 4

in that interval you would say
\[\frac{3\pi}{4},\frac{7\pi}{4}\]

Answer 5

thank you so much!!!! @satellite73