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. Identify the concept of coterminal angles: Coterminal angles are angles that share the same terminal side when drawn in standard position. They differ by a multiple of 360 degrees.
2. Find a coterminal angle for 765°: To find a coterminal angle between 0° and 360°, subtract 360° from 765° until the result is within this range. Start by calculating 765° - 360° = 405°, then 405° - 360° = 45°.
3. Recognize that 45° is a common angle: The angle 45° is a well-known angle in trigonometry, and its tangent value is often memorized.
4. Determine the tangent of 45°: The tangent of 45° is known to be 1, as tan(45°) = 1.
5. Conclude that tan(765°) = tan(45°): Since 765° is coterminal with 45°, the tangent of 765° is the same as the tangent of 45°, which is 1.