Answer:
b. 5/√21
Step-by-step explanation:
The sine is positive in quadrant II, so the cosecant will be also. The sine function never has a magnitude greater than 1, so the cosecant function (the reciprocal of the sine) never has a magnitude less than 1.
The only positive number with a magnitude greater than 1 among your answer choices is 5/√21, selection B.
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If you draw the triangle with hypotenuse 5 and side 2 along the x-axis, you find the Pythagorean theorem tells you the opposite side (parallel to the y-axis) has length ...
... O = √(5² -2²) = √21
Then the sine ratio is ...
... Sin = Opposite/Hypotenuse = (√21)/5
The cosecant function is the reciprocal of the sine function, so its value is ...
... csc(θ) = 1/sin(θ) = 1/((√21)/5)
... csc(θ) = 5/√21
