104k views
1 vote
The angle whose measure is (3pi)/4 terminates in quadrant || and its reference angle is for pi/4. what are the reciprocal trigonometric function values for (3pi)/4? check all that apply.

sec((3pi)/4) = - 1/2
sec((3pi)/4) = - sqrt(2)
csc((3pi)/4) = - sqrt(2)
cot ((3pi) /4 )=-1
csc((3pi)/4) = sqrt(2)

1 Answer

6 votes

Answer:

Options (2), (4) and (5)

Explanation:

An angle whose measure is
(3\pi )/(4) terminates in quadrant 2 and its reference angle is
(\pi)/(4).

As we know only Sine value of a reference angle which terminates in 2nd quadrant is positive. Tan and Cosine of this angle are negative.

Similarly, Cosec of a reference angle terminating in 2nd quadrant is positive while sec and cot values of the same angle are negative in the 2nd quadrant.


\text{Cosec}((3\pi)/(4))=\text{Cosec}((\pi)/(4))=√(2)


\text{Sec}(3\pi)/(4)=-\text{Sec}(\pi)/(4)=-√(2)


\text{Cot}((3\pi)/(4))=-\text{Cot}((\pi)/(4) )=-1

Therefore, Options (2), (4) and (5) will be the answer.

User Mohammad Jannesary
by
7.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories