Question

Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θ radians (where 0≤θ<2π). The circle's radius is 2.5 units long and the terminal point is (−2.26,1.07).What is the angle's measures (in radians)?θ=

Answer 1

The angle's measure in radians is calculated as: θ = 1.86π

What is the angle of the terminal point?

The circle's radius is 2.5 units long and the terminal point is (−2.26, 1.07).

The point (−2.26, 1.07) is in Q II and tan is negative.

Since the position in the 3-o'clock is basically the positive x-axis, this means the angle that is terminating at (2.26, -1.07) (which is in Q IV) should look like the given diagram.

from the right triangle we have

tan θ = 1.07/-2.26

tan θ = -0.4735

θ = tan⁻¹-0.4735

θ = 334.66°

In radians the angle is: 334.66° * π/180 = 1.86π

Answer 2

To solve this problem we can find the angle in terms of the trigonometric identities so we can use tg that is:

`tg(\theta)=(1.07)/(-2.26)`

and we solve for theta so:

`\begin{gathered} \theta=tg^(-1)(-0.47) \\ \theta=154.83 \\ \theta=0.86\pi \end{gathered}`

So the answer in radians is 0.86 pi