Tuesday, October 11, 2011
"Famous" angles practice
The "famous" angles in the first quadrant (and on the x-axis and y-axis adjacent to the first quadrant are 0°, 30°, 45°, 60° and 90°. You are expected to know the sine, cosine and tangent values for all these angles. When we move to the other quadrants, any angle that is 90° or 180° or 270° more than a famous angle will share trig values with one of the first quadrant angles or the value will be the negative. The mnemonic device is
All (all trig function are positive in the first quadrant)
Students (only sine is positive in the second quadrant)
Take (only tangent is positive in the third quadrant)
Calculus (only cosine is positive in the fourth quadrant)
The three "minor" trig functions, secant, cosecant and cotangent can all be defined as reciprocals of major trig functions.
secx = 1/cosx
cscx = 1/sinx
cotx = 1/tanx
Here are six problems dealing with "famous" angles. Remember that pi radians = 180°.
a) cos(630°)
b) sin(-7pi/3)
c) tan(7pi/6)
d) cot(-420°)
e) sec(225°)
f) csc(13pi/3)
Answers in the comments.
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a) cos(630°)
ReplyDelete630-360 = 270, so this is the same as cos(270°), which is 0.
b) sin(-7pi/3)
-7/3 = -2 1/3, so this is the same as sin(-pi/3), which means we are in the fourth quadrant. You can think of this angle as -60° or 300° if you prefer, and the value of sin is -sqrt(3)/2.
c) tan(7pi/6)
7/6 = 1 1/6, which means we are dealing with tangent in third quadrant, which is the same as tan(pi/6) or 30°, which is sqrt(3)/3.
d) cot(-420°)
add 360 to -420 and get -60. tangent at this angle is -sqrt(3) so cotangent is -1/sqrt(3), which we usually write as -sqrt(3)/3
e) sec(225°)
225° is the third quadrant opposite 45°. cos(45°) = sqrt(2)/2, so cos(225°) = -sqrt(2)/2 and secant is the reciprocal -sqrt(2).
f) csc(13pi/3)
13/3 = 4 1/3, so this angle is twice around the circle and stop at pi/3 or 60°. sin(60°) = sqrt(3)/2, so csc = 2/sqrt(3), which we write as 2sqrt(3)/3.
I went to Math lab and I have a better understanding I was working in degrees and need to work in radians and get more familiar with the unit circle. I just figured out how to solve for the law of sin and co-sine. yeah!
ReplyDeleteHi, Lashell. Glad you were able to get help in understanding this.
ReplyDelete