Final answer:
After evaluating each expression, sin(3π) and tan(900°) are the trigonometric values that equal 0. Cos(0°) equals 1, and cot(0°) is undefined.
Step-by-step explanation:
To determine which trigonometric values equal 0, we can evaluate each given expression.
sin(3π): Since the sine function has a period of 2π, sin(3π) is equivalent to sin(π), which equals 0.
cos(– 360°): The cosine function is periodic with a period of 360°, therefore cos(– 360°) is the same as cos(0°), which is 1, not 0.
tan(900°): The tangent function has a period of 180°. 900° is 180° × 5, so tan(900°) is tan(180° × 5), which is equivalent to tan(0°) and equals 0.
cot(0°): Cotangent is the reciprocal of the tangent function. Since tan(0°) = 0, the cot(0°) is undefined (not 0).
Therefore, the trigonometric values that equal 0 are sin(3π) and tan(900°).