Step by step
The question
Question: solve tan x = 1.
Find every angle from 0° up to 360°.
tan x = 1
We want the angles from 0° to 360°: one full turn.
0° ≤ x < 360°
1 Find the reference angle
From the unit circle: tan 45° = 1.
So the reference angle is 45°.
tan 45° = 1
2 Find every angle
Tan is positive in quadrants I and III.
45° and 180° + 45°: x = 45° or 225°.
tan x = 1: x = 45° or 225°
Careful!
The calculator gives only 45°.
But the line crosses the circle twice.
225° works too.
Careful: not only x = 45° ✗
On the circle: 2 points, so 2 angles.
So x = 45°, 225°.
x = 45°, 225°
3 Check
Let's check every answer in the equation.
Each one must give 1.
x = 45°: tan 45° = 1 = 1
x = 225°: tan 225° = 1 = 1
Every answer works.
So x = 45°, 225°.
Let's look back.
First: find the reference angle.
Then: find every angle.
Last: check.
Answer
x = 45°, 225°