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Multiple Choice
For each expression, identify which coterminal angle to use & determine the exact value of the expression. tan765°
A
−1
B
1
C
0
D
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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.
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°.
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°).
Step 4: Recall the exact value of tan(45°). The tangent of 45° is a well-known trigonometric value, which is 1.
Step 5: Conclude that the exact value of tan(765°) is the same as tan(45°), which is 1.