Here's a theorem about the tangent function

[imdapolak]

1. Here's a theorem about the tangent function. tan(x) = c iff 1: x = tan^-1*c or 2: x = tan^-1*c+n(180) for some integer n. Find a solution to tan x = 1 between 270 and 450 degrees.




2.


3. I am not really sure how to go about starting this problem. I have only two problems in my homework, but no solution to either to self check.

 

[slider142]

The way I would go about solving this is to first find an expression for all values of x that satisfy the equation, and then locate the specific x that falls in that range. They give you the general solution for c in the first sentence. In your case, c = 1.

 

[HallsofIvy]

In other words, find one angle such that tan x= 1 and if it is not between 270 and 450 degrees add 180 degrees until it is. I suppose you could use a calculator but since tan(x)= sin(x)/cos(x), tan(x)= 1 is the same as sin(x)= cos(x). It should be easy to find one angle x such that sin(x)= cos(x).