For each expression, identify which coterminal angle to use & determine the exact value of the expression.
$\tan765\degree$

• A. $-1$
• B. $1$
• C. $0$
• D. undefined

Answer: (B)

Verified step by step guidance

1. Step 1: Understand that coterminal angles are angles that share the same terminal side. To find a coterminal angle, you can add or subtract multiples of 360° from the given angle.
2. Step 2: For the angle 765°, find a coterminal angle by subtracting 360° until the angle is between 0° and 360°. Start by calculating 765° - 360° = 405°, and then 405° - 360° = 45°.
3. Step 3: Recognize that the tangent function, tan(θ), is periodic with a period of 180°. This means tan(θ) = tan(θ + 180°k) for any integer k. Therefore, tan(765°) = tan(45°).
4. Step 4: Recall the exact value of tan(45°). The tangent of 45° is a well-known trigonometric value, which is 1.
5. Step 5: Conclude that the exact value of tan(765°) is the same as tan(45°), which is 1.