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

Answer:

$\dfrac{5}{3}$

Step-by-step explanation:

We know that $\sec{\theta}=\dfrac{1}{\cos{\theta}}$. 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

$\left[\dfrac{4}{5}\right]^2+\cos^2 \theta = 1 \Rightarrow \\\\\\\quad \cos^2 \theta = 1-\dfrac{16}{25}=\dfrac{9}{25} \Rightarrow\\ \\\cos \theta = \pm \dfrac{3}{5}$

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

$\cos{\theta}=\dfrac{3}{5} \quad \Rightarrow \quad \sec \theta=\dfrac{1}{\cos\theta}=\dfrac{5}{3}$