Question

write the ratios for sin m, cos m, and tan m. give the exact value and a four - decimal approximation.
(sin m=\frac{sqrt{39}}{20}) (type an exact answer in simplified form. type an integer or a fraction.)
(sin m = 0.3122) (type the decimal approximation of the answer rounded to four decimal places. round the final answer to four decimal places as needed.)
(cos m=\frac{19}{20}) (type an exact answer in simplified form. type an integer or a fraction.)
(cos m=square) (round the final answer to four decimal places as needed.)
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Explanation:

Step1: Recall cosine definition

In a right triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle M\), adjacent side is \(19\), hypotenuse is \(20\). So \(\cos M = \frac{19}{20}\).

Step2: Convert to decimal

Divide \(19\) by \(20\): \(19\div20 = 0.95\). Rounded to four decimal places, it's \(0.9500\).

Answer:

Exact value: \(\frac{19}{20}\), Decimal approximation: \(0.9500\)