Convert the angle 236.345° to DMS notation (by breaking down the decimals into
minutes and seconds):
236°0.345°60' /1°
236°20.7' 236°20' 0.7' 60' /1'
236° 20' 42"
Convert the angle 236.345° to radians (convert the entire amount into radians by
multiplying πradians by 180°, which is actually equal to “1” since, from above, 180°
πradians):
236.345°πradians/180°(236.345 3.141592) radians/180°
4.124998 radians
And, conversely, convert 4.124998 radians to degrees:
4.124998 radians 180°/3.141592
236.345°What are the six trigonometric functions?
There are six basic trigonometric functions that can be used to interpret the measure-
ment of angles and triangles—most often defined as circle trig definitions. In terms of
the illustration below, the following lists the six trig functions of , all defined in
terms of the coordinates of Q (x, y):
- cos
x - sin
y - tan
y/xif x
0 - sec
1/xif x
0 - csc
1/yif y
0 - cot
x/yif y
0
The full names for these functions are cos (cosine); sin (also seen as “sine”); tan
(tangent); sec (secant); csc (cosecant); and cot (cotangent).
How are trigonometric functionsused to describe a right triangle?
The trigonometric functions can be interpreted using the illustration on p. 202 of a
right triangle. If is the angle (see illustration), ais one leg (called the adjacent
because it is adjacent to the angle), bis another leg (called the opposite,because it is
opposite the angle), and cis the hypotenuse:
- cos
a/cadjacent/hypotenuse - sin
b/copposite/hypotenuse - tan
b/aopposite/adjacent - sec
c/ahypotenuse/adjacent - csc
c/bhypotenuse/opposite - cot
a/badjacent/opposite 201