Question

Select the correct answer from each drop-down menu.

Angle θ lies in the second quadrant, and sin θ = .​

Answer 1

Cos θ = -4/5

Tan θ = -3/4

Step-by-step explanation:

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Answer 2

Cos θ = -4/5

Tan θ = -3/4

Explanation:

The question is as following:

Select the correct answer from each drop-down menu.

Angle θ lies in the second quadrant, and sin θ =3/5.

cos θ = -4/5, -3/5, 3/5, 4/5

tan θ = -4/3, -3/4, 3/4, 4/3

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Since, the angle lies in second quadrant (negative x axis and positive y axis) we can deduce that cos θ is negative and tan θ is also negative.

If sin θ =3/5

`cos \ \theta =√(1-sin^2 \theta) = \sqrt{1-((3)/(5) )^2} =\sqrt{1-(9)/(25) }=\sqrt{(16)/(25) } =(4)/(5)`

∴ Cos θ = -4/5 ⇒ because θ lies in the second quadrant.

And

Tan θ = (sin θ)/(cos θ) = (3/5) / (-4/5) = -3/4.