Question

If sin theta = -4/5 and theta is in quadrant 4, the value of sec theta is _____. If necessary, use the slash mark (/) for a fraction bar.

Answer 1

5/3 is the correct answer

Explanation:

a p e x

Answer 2

`(5)/(3)`

Explanation:

What we need to find

• We are given that sin theta=-4/5
• It is also in the 4th quadrant.
• Our problem is that there isn't a known or straight to identity invlonlving sin and sec so we need to use a series of trig identies to find this answer.

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.

1. 
   `\sin {}^(2) (x) + \cos {}^(2) (x) = 1`

where x is theta.

Plug in -4/5 for x in sin squared.

`\sin {}^(2) ( - (4)/(5) ) + \cos {}^(2) (x) = 1`

`\sin( (16)/(25) ) + \cos {}^(2) (x) = 1`

`\cos {}^(2) (x) = 1 - (16)/(25)`

`cos {}^(2) (x) = (9)/(25)`

`\cos(x) = (3)/(5)`

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.

`\sec(x) = (5)/(3)`