Answer:
[tex] \frac{5}{3} [/tex]
Step-by-step explanation:
What we need to find
Sec and cos are reciprocal identies and sin and cos are pythagorean identies so we can use those.Use the pythagorean identies to find cosine.
where x is theta.
Plug in -4/5 for x in sin squared.
[tex] \sin {}^{2} ( - \frac{4}{5} ) + \cos {}^{2} (x) = 1[/tex]
[tex] \sin( \frac{16}{25} ) + \cos {}^{2} (x) = 1[/tex]
[tex] \cos {}^{2} (x) = 1 - \frac{16}{25} [/tex]
[tex] cos {}^{2} (x) = \frac{9}{25} [/tex]
[tex] \cos(x) = \frac{3}{5} [/tex]
cosine in the 4th quadrant is positve so 3/5 is cosine of theta.
Cosine and secant are reciprocal so just flip the numbers to find the secant.
[tex] \sec(x) = \frac{5}{3} [/tex]
