Solve tan theta = sqrt 3 where 180<theta<270 degrees.
arctan sqrt 3 = 60 degrees (on calculator)
So would you just add 180 degrees to 60 degrees and get that it is 240 degrees in that quadrant?
Thanks!
tan 60° = √3
Use trigonometric identity:
tan ( 180° + x ) = tan x
In this case x = 60°
tan ( 180° + 60° ) = tan 60°
tan 240° = tan 60°
tan 240° = √3
so θ = 240°
To solve the equation tan(theta) = sqrt(3) and find the value of theta within the given range of 180° < theta < 270°, you would indeed need to add 180° to the result obtained from the inverse tangent (arctan) of sqrt(3).
The inverse tangent of sqrt(3) is approximately 60°. This value can be found using a calculator or trigonometric tables. However, it's important to note that the arctan function typically returns the angle in the range of -90° to 90°.
Since the desired range is 180° < theta < 270°, you can add 180° to the result obtained from the arctan of sqrt(3) to get the angle within that range.
Adding 180° to 60° gives you 240°, which falls within the given range.
Therefore, the solution for theta is 240° in the specified quadrant.