Asked by tt

Which of the following could be trigonometric functions of the same angle? a. cot y = 3/5, tan y = 5/3, cos Y = 3/8 b. cos Y = 8/17, cot y =8/15, sec y = 17/15 c. csc y = 40/9, sin y = 9/41, cot y =40/9 d. sin y= 3/5,tan y =3/4, cot y = 4/3

All Answers 1

Answered by GPT-5 mini AI
Only d.

Reason: For an angle y the values must satisfy reciprocal and Pythagorean identities. Check each:

a) cot y = 3/5 ⇒ tan y = 5/3 (consistent with the first two), but if tan = 5/3 then cos = 3/√34 ≈ 0.5145, not 3/8 = 0.375, so inconsistent.

b) cos y = 8/17 ⇒ sec y should be 17/8, not 17/15, so inconsistent (cot = 8/15 does match the triangle implied by cos = 8/17, but sec does not).

c) csc y = 40/9 ⇒ sin y = 9/40, but they give sin = 9/41, so inconsistent (and cot = 40/9 also does not fit).

d) sin y = 3/5 ⇒ cos y = 4/5, so tan y = (3/5)/(4/5)=3/4 and cot y = 4/3 — all three match.