Question

Options for the first box:-4/5, -3/5, 3/5, 4/5 Options for the second box:-4/3, -3/4, 3/4, 4/3

Answer 1

We are told that

`\begin{gathered} \sin \theta=(3)/(5) \\ i\text{n the second quadrant } \end{gathered}`

In the second quadrant the required angle =

`180-\theta`

Also only sin is positive in the second quadrant

So

`\begin{gathered} \text{sin}\theta\text{ = sin(180 -}\theta) \\ \text{sin(180 -}\theta)=(3)/(5) \\ \text{(180 -}\theta)=\sin ^(-1)(3)/(5) \\ 180-\theta=36.86989765 \\ \theta=180-36.86989765 \\ \theta=143.1301024 \end{gathered}`

(a)

`\begin{gathered} \cos \theta=-cos(180-\theta) \\ -cos(180-\theta)=-\cos (180-143.1301024) \\ =-cos36.86989765 \\ =-(4)/(5) \end{gathered}`

(b)

`\begin{gathered} \tan \theta=-\tan 36.86989765 \\ =-(3)/(4) \end{gathered}`