FInd exact value of the expression Sec(arctan -5/12)

[NoAsherelol]

Hey guys i want to know if i am correct here

let y=arctan(-5/12)

sec y= 13/12 or 65 degrees

is this correct

 

[tkhunny]

Tangent is negative in Quadrants I and IV. This eliminates your approximate 65º.
The problem statement asked for an exact value. This eliminates your approximate 65º.
The Range of the secant function is NOT an angle. This eliminates your approximate 65º.

All such problems require only a right triangle and a few definitions.

There is an angle whose tangent is 5/12.

Ths cosine of that angle, whatever it is, is 12/13. The Pythagorean Theorem tells us this.

Now you need only a few definitions.

sec(x) = 1/cos(x)

The RANGE of the arctangent function is (-pi/2,pi/2). This eliminates Quadrant II.

Cosine and secant are positive in Quadrant IV.

That's it. Just put it all together.