Question

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)

Answer 1

Answer:

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

Step-by-step explanation:

An angle whose measure is $\frac{3\pi }{4}$ terminates in quadrant 2 and its reference angle is $\frac{\pi}{4}$.

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.

$\text{Cosec}(\frac{3\pi}{4})=\text{Cosec}(\frac{\pi}{4})=\sqrt{2}$

$\text{Sec}\frac{3\pi}{4}=-\text{Sec}\frac{\pi}{4}=-\sqrt{2}$

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

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