Question

Consider that sin θ = 0.819.Select Yes or No to tell whether the statement is possible.

A. Cos θ=0.819B. cos θ= -0.574 C. cos θ= 0.574

Answer 1

A. No

B. Yes

C. Yes

Explanation:

Given that:

`\sin\theta\approx0.819`

First, find an approximate value for θ.

`\theta=\arcsin(0.819)\approx54.98\degree`

• Sine is positive in the first and second quadrant.

,

• Cosine is positive in the first quadrant and negative in the second quadrant.

`\begin{gathered} \text{ In the first quadrant: }\cos54.98\approx0.574 \\ \text{ In the second quadrant:}\cos(180-54.98)=-\cos54.98=-0.574 \end{gathered}`

Therefore, we have Options B and C to be possible. i.e.

• A. No

,

• B. Yes

,

• C. Yes