Question

Determine the function that satisfies the following conditions.Find sin θ when cos θ= 0.695 and tan θ< 0.

Answer 1

The given function is

`cos\theta=0.695`

Given that tan θ <0

Notice that the given cosine is positive

Hence the angle is in the first and fourth quadrant

Since it is given that tan θ <0, this implies that tan is negative

Since tan is negative in second and fourth quadrant then the fourth quadrant will be used to defined the value of sine

From the given function

The value of θ is

`\begin{gathered} \theta=\cos^(-1)0.695 \\ \theta=45.97 \end{gathered}`

Hence the value of the angle in the fourth quadrant is:

`\theta=360-45.97=314.03`

Hence the value of sin θ is

`\begin{gathered} sin\theta=sin(314.03) \\ =-0.7190 \end{gathered}`