Question

There are multiple graphs, so I just need the drawing of the graph and explanation!!

Answer 1

GIVEN:

The cosine of the angle is:

`\cos \theta=(4)/(7)`

SOLUTION:

To find the measure of the angle, we can find the cos inverse of 4/7. Using a calculator:

`\begin{gathered} \text{If }\cos \theta=(4)/(7), \\ \text{then} \\ \theta=\cos ^(-1)((4)/(7)) \\ \theta=55.15\degree \end{gathered}`

The problem gives that sin θ is negative and we can see that cos θ is positive. The image below shows which angles are positive and in which quadrant:

Therefore, the angle is in the 4th quadrant.

In the fourth quadrant, the value of the angle is:

`\theta_1=360-\theta`

Therefore, the angle will be:

`\begin{gathered} \theta_1=360-55.15 \\ \theta_1=304.85\degree \end{gathered}`

The angle is 304.85°