Question

Evaluate the function without using a calculator.
sec 210 degrees

Answer 1

sec = 1/cos

so this is 1/cos(210)

we know cos(180) is -1, 210 degrees is 30 degrees into the 3rd quadrant coming from the x-axis, rotating counter-clockwise. we know that cos(30) = sqrt(3)/2

Answer 2

Can you do the rest?

Answer 3

Check this out. You need to memorize this unit circle.

Answer 4

oh i kinda get it.....so i just draw the triangle? how about tan 330?

Answer 5

You know that the unit circle is 360 degrees (2pi). 360-330 = 30 degrees. So, you are going 330 degrees counter-clockwise around the unit circle. In reverse, you are going 30 degrees clockwise. Since you know tan = sin/cos, you are really finding sin(330)/cos(330). You know that sin is negative in the 4th quadrant; so sin(330) = -sin(30). You know cos is positive in the 4th quadrant, so cos(330) = cos(30). So, what is -sin(30)/cos(30? Well, we already found that cos(30) = sqrt(3)/2. sin(30) is 1/2. But, this is -sin, so it's \[\frac{-\frac{1}{2}}{\frac{\sqrt{3}}{2}} = -\frac{1}{2}\times\frac{2}{\sqrt{3}} = -\frac{1}{\sqrt{3}} = -\frac{\sqrt{3}}{3}\]

Answer 6

Memorize all the values for sin and cos in the 1st quadrant of the unit circle. Then apply that knowledge to your understanding of the circle and basic trig identities. You can draw the circle out on any test and follow similar procedures as we did here to find your answers. It takes time, but it gets useful!

Answer 7

i wouldnt mind u drawing the circle for me....gives me a better understanding on how to do the prob

Answer 8

^ 5 posts up, the circle is attached

Answer 9

http://assets.openstudy.com/updates/attachments/53756a62e4b058cfb0da76a4-digitallogic-1400204233493-screenshot20140515at20.26.48.png