Which Calculator Mode for Trigonometry: Radians or Degrees?

[gillgill]

Need help...
secx=3.45 (0<=x<=2pi) (Accurate to 2 decimal places)
secx=-5.2 (0<=x<=2pi) (Accurate to 2 decimal places)

How do you do these questions?...i am getting mixed up by doing it on the calculator...use radian or degrees mode??...cos or cos-1?...and also about csc and cot too...can anybody explain thoroughly how to do them? (Maybe give more examples)

Thanks

 

[vsage]

the domain of x (0<=x<=2$$\pi$$) suggests to me that x is in radians. Also, consider what sec(x) is in terms of sin(x) and cos(x). Keep in mind that $$sec^{-1}(sec(x)) = x$$ where $$sec^{-1}(x)$$ is the inverse function of sec(x). If your calculator doesn't have one of those buttons, try and fiddle around and find sec(x) in terms of cos(x) as well as the inverse of sec(x) in terms of the inverse of cos(x). Same thing with the other 2 trig functions you gave.

 

[gillgill]

and also...Solve: tanx=3.2, 0≤x≤2π
how do you know is it tan-1(3.2) or tan(3.2)?

 

[whozum]

Draw a triangle. Tan = Opp/Adj. So 3.2 = Opp and Adj = 1. You are solving for the angle x on the horizontal at the hypotenuse. The only way to get this angle is to take the arctangent of the ratio of sides, 3.2:1

In short, the easiest way that I can think of to go from tan(x) to x is to get an arctangent. tan(3.2) will tell you the ratio of the sides given an angle of 3.2 (radians or degrees)


tan(x) = 3.2

arctan(tan(x)) = arctan(3.2)

x = arctan(3.2)

 

[gillgill]

secx=3.45 (0<=x<=2pi)...does that mean (radians) cos(3.45) and then take the inverse??

 

[whozum]

$$sec(x) = \frac{1}{cos(x)}$$

$$cos(x) = \frac{Adj}{Hyp}$$

From this, draw the triangle with the sides labeled accordingly. If you mess up it iwll probably be here, so be sure to list your steps if you have trouble.

Once you draw your triangle, figure out what cos(x) should be, then take the arccosine to find x.

 

[gillgill]

for secx=-5.2 (0<=x<=2pi) (Accurate to 2 decimal places)...i found out that the answer is 1.76...how do you know if there is one answer or two answers?

 

[whozum]

Draw the triangle on a coordinate plane, and see if there is more htan one possible answer answer.
For sec(x) -5.2/1, one unit in the -x direction, and 5.2 in the positive y direction, or 1 unit in the positive x direction, and negative 5.2 in the y direction.

This is for thei nterval 0-2pi