n angle theta satisfies the relation (CSC theta)(cos theta)=-1 Give an example of information needed to determine a unique value for theta If sec theta is known to be negative, what is the CSC theta value of theta?
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To determine a unique value for theta in the given relation (CSC theta)(cos theta) = -1, we need to know the sign of the sec(theta) value.
If sec(theta) is known to be negative, it means that the cosine function (cos(theta)) is negative. This is because sec(theta) is the reciprocal of the cosine function (sec(theta) = 1/cos(theta)).
With the knowledge that cos(theta) is negative, we can determine the value of theta by finding the reciprocal of sine (CSC) that satisfies the equation.
Since the product of a negative value (cos(theta)) and a negative reciprocal value (CSC(theta)) equals -1, the sine function (CSC(theta)) must be positive.
Therefore, the CSC(theta) value of theta when sec(theta) is negative is positive.