Question

Can someone please help me with this problem?

Answer 1

`sin(\theta)=(40)/(41) \\cos(\theta)=(9)/(41) \\tan(\theta)=(40)/(9)\\csc(\theta)=(41)/(40) \\sec(\theta)=(41)/(9) \\cot(\theta)=(9)/(40)`

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=√(729) \\x=27`

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

`sin(\theta)=(opp)/(hyp) = (120)/(123) =(40)/(41) \\cos(\theta)=(adj)/(hyp) = (27)/(123) =(9)/(41) \\tan(\theta)=(opp)/(adj) = (120)/(27) =(40)/(9)\\csc(\theta)=(41)/(40) \\sec(\theta)=(41)/(9) \\cot(\theta)=(9)/(40)`