Answer:
Step-by-step explanation:
Hypotenuse: The longest side in the triangle and it is opposite to 90°
Opposite Side: The side oppoiste to the angle.
Adjacent side: The side next to the angle.
First find 'c' using Pythagorean theorem,
c² = 9² + 12²
= 81 + 144
= 225
c =√225
c = 15
[tex]\sf \ Sin \ \theta = \dfrac{opposite \ side \ of \ \theta}{hypotenuse}= \dfrac{12}{15}[/tex]
[tex]\sf \ Cos \ \theta = \dfrac{adjacent \side \ of \ \theta}{hypotenuse}= \dfrac{9}{15}\\\\ Tan \ \theta= \dfrac{opposite \ side \ of \ \theta}{adjacent \ side \ of \ \ theta}= \dfrac{12}{9}[/tex]
[tex]\sf \ Csc \ \theta= \dfrac{hypotenuse}{opposite \ side \ of \ \ theta}= \dfrac{15}{12}\\\\\ Sec \ \theta = \dfrac{hypotenuse}{adjacent \ side \ of \ \theta}= \dfrac{15}{9}\\\\Cot \ \theta= \dfrac{adjacent \ side \ of \ \theta}{opposite \ side \ of \ \theta}= \dfrac{9}{12}[/tex]
[tex]\sf \ Sin \ \alpha = \dfrac{opposite \ side \ of \ \alpha \theta}{hypotenuse}= \dfrac{9}{15}[/tex]
[tex]\sf \ Cos \ \alpha = \dfrac{adjacent \side \ of \ \alpha }{hypotenuse}= \dfrac{12}{15}\\\\ Tan \ \alpha = \dfrac{opposite \ side \ of \ \alpha }{adjacent \ side \ of \ \ theta}= \dfrac{9}{12}[/tex]
[tex]\sf \ Csc \ \alpha = \dfrac{hypotenuse}{opposite \ side \ of \ \alpha }= \dfrac{15}{9}\\\\\ Sec \ \alpha \theta = \dfrac{hypotenuse}{adjacent \ side \ of \ \alpha }= \dfrac{15}{12}\\\\Cot \ \alpha = \dfrac{adjacent \ side \ of \ \alpha }{opposite \ side \ of \ \alpha }= \dfrac{12}{9}[/tex]
