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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 the concept of coterminal angles. Coterminal angles are angles that share the same terminal side when drawn in standard position. To find a coterminal angle, you can add or subtract multiples of 360° to the given angle.
Step 2: Simplify the given angle, 765°, by subtracting 360° repeatedly until the resulting angle is between 0° and 360°. This will give you the coterminal angle.
Step 3: Once you have the coterminal angle, determine the reference angle. The reference angle is the acute angle formed by the terminal side of the angle and the x-axis. Use the quadrant of the coterminal angle to determine the sign of the tangent function.
Step 4: Recall the tangent function, tan(θ), which is defined as the ratio of the sine of the angle to the cosine of the angle: . Use the reference angle and the quadrant to determine the exact value of tan(765°).
Step 5: Evaluate the tangent function for the reference angle, applying the correct sign based on the quadrant. This will give you the exact value of tan(765°).