Verified Answer :

Cos N = 3/5
Sin N = 4/5
Tan N = 4/3
Sin P = 9/15 or 3/5
Cos P = 12/15 or 4/5
Tan P = 9/12 or 3/4

The value of cosN, sinN, tanN, sinP, cosP, and tanP are 3/5, 4/5, 4/3, 3/5, 4/5, and 3/4

What is the trigonometric ratio?

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

We have a right triangle shown in the picture.

For cosN it is the ratio of the side adjacent to the angle N to the hypotenuse.

The side adjacent = 9 and hypotenuse = 15

\(\rm CosN = \frac{9}{15} \Rightarrow \frac{3}{5}\)

For sinN it is the ratio of the side opposite to the angle N to the hypotenuse.

The side opposite = 12 and hypotenuse = 15

\(\rm SinN= \frac{12}{15} \Rightarrow \frac{4}{5}\)

For tanN it is the ratio of the side opposite to the angle N to the hypotenuse.

\(\rm TanN = \frac{12}{9} \Rightarrow \frac{4}{3}\)

Similarly, we can find the sinP, cosP, and tanP

\(\rm SinP =\frac{9}{15} \Rightarrow \frac{3}{5}\)

\(\rm CosP =\frac{12}{15} \Rightarrow \frac{4}{5}\)

\(\rm TanP =\frac{9}{12} \Rightarrow \frac{3}{4}\)

Thus, the value of cosN, sinN, tanN, sinP, cosP, and tanP are 3/5, 4/5, 4/3, 3/5, 4/5, and 3/4

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