Mathematics: Can someone please help me with this problem?

Can someone please help me with this problem?

Ответ:

blackbetty79

10.02.2022

$sin(\theta)=\frac{40}{41} \\cos(\theta)=\frac{9}{41} \\tan(\theta)=\frac{40}{9}\\csc(\theta)=\frac{41}{40} \\sec(\theta)=\frac{41}{9} \\cot(\theta)=\frac{9}{40}$

Step-by-step explanation:

Notice we can use the Pythagorean theorem to find the measure of the unknown side via:

$123^2=120^2+x^2\\x^2=729\\x=\sqrt{729} \\x=27$

and now, knowing all the sides, we can find all te trigonometric functions of the angle $\theta$ :

$sin(\theta)=\frac{opp}{hyp} = \frac{120}{123} =\frac{40}{41} \\cos(\theta)=\frac{adj}{hyp} = \frac{27}{123} =\frac{9}{41} \\tan(\theta)=\frac{opp}{adj} = \frac{120}{27} =\frac{40}{9}\\csc(\theta)=\frac{41}{40} \\sec(\theta)=\frac{41}{9} \\cot(\theta)=\frac{9}{40}$