If tan(x) = 1, what is the value of x in the interval [0°, 360°)?

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Question: If tan(x) = 1, what is the value of x in the interval [0°, 360°)?

Options:

Correct Answer: 45°

Solution:

tan(x) = 1 at x = 45° and 225°; in the interval [0°, 360°), the first solution is 45°.

If tan(x) = 1, what is the value of x in the interval [0°, 360°)?

If tan(x) = 1, what is the value of x in the interval [0°, 360°)?

Step 1: Understand that tan(x) = 1 means we are looking for angles where the tangent function equals 1.
Step 2: Recall that the tangent function is equal to 1 at specific angles in the unit circle.
Step 3: The first angle where tan(x) = 1 is 45° because at this angle, the opposite and adjacent sides of the triangle are equal.
Step 4: The tangent function is periodic, meaning it repeats its values. The next angle where tan(x) = 1 is found by adding 180° to 45°, which gives us 225°.
Step 5: Check the interval [0°, 360°). The angles we found are 45° and 225°. Both are within this interval.
Step 6: Since the question asks for the first solution in the interval, we choose 45°.

Trigonometric Functions – Understanding the properties and values of the tangent function, particularly where it equals 1.
Unit Circle – Using the unit circle to determine angles corresponding to specific trigonometric values.
Interval Notation – Recognizing and applying the specified interval [0°, 360°) to find valid solutions.