Question

Given theta = 7pi/6, find (sec theta, cos theta)

Answer 1

Make a sketch of the angle on some coordinate axes. What is the reference angle?

Answer 2

Doesn't give me one. That's the way the problem is typed on the worksheet.

Answer 3

I know...that's why you draw the angle and figure out the reference angle.

Answer 4

(The reference angle is the smallest angle you can draw to the \(x\) axis once you've plotted it on axes)

Answer 5

Some people let the pi part confuse them. Remember 7/6 is a bit bigger than one, so 7pi/6 will be a bit bigger than pi. Where is pi on the unit circle? 7pi/6 will be pi/6 beyond that.

Answer 6

Yep. You can also think of it like this:\[\frac{7\pi}{6} = \frac{6\pi}{6} + \frac{1\pi}{6} = \pi + \frac{\pi}{6}\]

Answer 7

I see that 7pi/6 is 210 degrees according to the unit circle. Since it's sec and cos, the answers both have to be positive correct?

Answer 8

Nope. 7pi/6 will be in quadrant III. In quadrant 3 both the cosine and secant are negative (as are the sine and cosecant, for that matter).

Answer 9

Glad I asked. Thanks

Answer 10

The unit circle is your friend. Always draw a unit circle.
7pi/6 (or 210 degrees) is over on the left side of the y axis and below the x-axis. therefore the x coordinate (which gives cosine) and the y-coordinate (which gives sine) are both negative.
Really, really, really, The unit circle is your friend. Invite him over for dinner; take him out to a show.

Answer 11

Lol awesome.