Question 4.2.5: Using Quotient and Reciprocal Identities Given sin t = 2/5 a...
Using Quotient and Reciprocal Identities
Given \sin t=\frac{2}{5} and \cos t=\frac{\sqrt{21}}{5}, find the value of each of the four remaining trigonometric functions.
We can find tan t by using the quotient identity that describes tan t as the quotient of sin t and cos t.
We use the reciprocal identities to find the value of each of the remaining three functions.
\csc t=\frac{1}{\sin t}=\frac{1}{\frac{2}{5}}=\frac{5}{2}
\cot t=\frac{1}{\tan t}=\frac{1}{\frac{2}{\sqrt{21}}}=\frac{\sqrt{21}}{2} We found \tan t=\frac{2}{\sqrt{21}}. We could use \tan t=\frac{2 \sqrt{21}}{21} but then we would have to rationalize the denominator.
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