How to solve tan ϑ + 1 = 0 in the domain 0 ≤ ϑ ≤ 3600? if i were to sit in an exam without calculator with this question, how can i solve it? Tips please :)
1 Answer
By using the 360+ϑ method.
Explanation:
Basically, the question that is asked is to find ϑ within the range of 0 and 3600 (degrees I am assuming). First, let's find out what ϑ is the domain of 0 to 360.
The only values for which tan ϑ can be -1 are 135 and 315 degrees. Now that we have these 2 values for 0 to 360, we need to evaluate them from 0 to 3600.
Since 3600 is just 10 times of 360, there are a total of 9 more sets of 360 degrees, or 18 different angles.
So, all that's necessary is continually adding 360 to the degree values that you currently have. This is possible because 360 + ϑ, is simply ϑ, and any multiple of 360 + ϑ, is simply ϑ as well.
So, go on adding multiples of 360 to the angles, until you reach the value closest to 3600, then stop. For example:
135 + 360= 495 315 + 360= 675
495 + 360= 755 675 + 360= 1035
