Question

If sin theta = -4/5 and theta is in quadrant 4, the value of sec theta

Answer 1

sec theta would be 5/3

Answer 2

`(5)/(3)`

Explanation:

We know that
`\sec{\theta}=(1)/(cos(\theta))`. On the other hand,

we can use the equality

`\sin^2 \theta + \cos^2 \theta=1`

to find the absolute value of
`\cos \theta`. It holds that

`\left[(4)/(5)\right]^2+\cos^2 \theta = 1 \Rightarrow \\\\\\\quad \cos^2 \theta = 1-(16)/(25)=(9)/(25) \Rightarrow\\ \\\cos \theta = \pm (3)/(5)`

Now, in the quadrant 4 the values of cosine is positive for all theta, hence

`cos(\theta)=(3)/(5) \quad \Rightarrow  \quad \sec \theta=(1)/(\cos\theta)=(5)/(3)`