Trigonometric Functions — Test

Question 13 • Mathematics III

Haruto simplified the value. cosecant of open paren 19 pi over 4 close paren is equal to square root of 2 Which statement explains whether Haruto is correct?

Answer

Haruto is not correct because the angle is coterminal with 3 pi over 4 , and cosecant of open paren 3 pi over 4 close paren is equal to the fraction with numerator negative 1 and denominator square root of 2 is equal to the fraction with numerator negative square root of 2 and denominator 2 .

Haruto is not correct because the angle is coterminal with pi over 4 , and cosecant of open paren pi over 4 close paren is equal to the fraction with numerator 1 and denominator square root of 2 is equal to the fraction with numerator square root of 2 and denominator 2 .

Haruto is correct because the angle is coterminal with 3 pi over 4 and the reference angle is pi over 4 .

Haruto is correct because the angle is coterminal with pi over 4 , which is also the reference angle.

Explanation

Subtract 4π from 19π/4 to get 3π/4, so the angles are coterminal. The angle 3π/4 lies in Quadrant II and has reference angle π/4, where sine is √2/2. Thus cosecant(3π/4) = 1/(√2/2) = √2, so Haruto is correct, as choice A states.

AI-written and checked against the verified answer.

More from this Course

Test

Test

Test