1) Which angle is not coterminal with 120 degrees? A) 840 B) -240 C) 480 2) Using the unit circle and the reference angle, identify the correct trigonometric value when theta is -90 degrees.A) Cos(theta) = undefined B) Sin(theta) = -1 C) Tan(theta) = 0

1) To determine which angle is not coterminal with 120 degrees, one must understand what coterminal angles are. Coterminal angles are angles that share the same terminal side when drawn in standard position. Every 360 degrees represents a full rotation, so to find coterminal angles you can add or subtract multiples of 360 degrees.

Let's examine each option: A) 840 degrees: To see if this is coterminal with 120 degrees, subtract 360 until you get an angle between 0 and 360 degrees. 840 - 360 = 480 480 - 360 = 120 Since we arrived at 120 degrees, 840 degrees is coterminal with 120 degrees.

B) -240 degrees: To see if this is coterminal, add 360 until you get a positive angle. -240 + 360 = 120 Since we arrived at 120 degrees, -240 degrees is coterminal with 120 degrees.

C) 480 degrees: Similar to the first example, subtract 360 degrees. 480 - 360 = 120 Since we arrived at 120 degrees, 480 degrees is coterminal with 120 degrees.

All provided angles A), B), and C) are coterminal with 120 degrees, which means we do not have a correct option that is not coterminal with 120 degrees based on the given choices.

2) To find the trigonometric values when theta is -90 degrees, you need to refer to the unit circle: A) Cos(theta) = undefined: The cosine of an angle corresponds to the x-coordinate on the unit circle. When theta is -90 degrees, the terminal side lies along the negative y-axis where the x-coordinate at that point is 0. Cosine is defined for all real numbers, so this option is incorrect since cosine should be 0, not undefined.

B) Sin(theta) = -1: The sine of an angle corresponds to the y-coordinate on the unit circle. When theta is -90 degrees, the terminal side lies on the circumference of the unit circle at the point (0, -1). So, Sin(-90 degrees) = -1, which is correct.

C) Tan(theta) = 0: The tangent of an angle is the ratio of the sine and cosine. When theta is -90 degrees and since cosine is 0 and sine is -1, the tangent is undefined because division by zero is not defined. So this option is incorrect.

The correct trigonometric value when theta is -90 degrees is B) Sin(theta) = -1.