R x y z 22 - UTEP
4.4 Trigonometric Functions of Any Angle
Definition of Trig Functions of Any Angle ¨C Let ¦È be an angle in standard position with (x, y) a point on
the terminal side of ¦È and r ?
x2 ? y 2 ? 0 .
y
x
cos ? ?
tan ? ?
r
r
r
r
csc ? ? , y ? 0 sec ? ? , x ? 0 cot ? ?
y
x
sin ? ?
y
, x?0
x
x
, y?0
y
Examples: The point is on the terminal side of an angle in standard position. Determine the exact values
of the six trigonometric functions of the angle.
1. (8, 15)
2. (-4, 10)
Examples: State the quadrant in which ¦È lies.
1. sin ? ? 0 and cos? ? 0
2. sin ? ? 0 and cos? ? 0
Example: Find the values of the six trig functions of ¦È with the given constraint.
1. cos ? ?
8
with tan ? ? 0
17
2. sec? ? ?2 with sin ? ? 0
Definition of Reference Angle ¨C Let ¦È be an angle in standard position. Its reference angle is the acute
angle ¦È¡¯ formed by the terminal side of ¦È and the horizontal axis.
Examples: Find the reference angle and sketch both angles.
1. ? ? 309
2. ?215
3. ? ?
7?
6
4. ? ? 11.6
Evaluating Trigonometric Functions of Any Angle ¨C To find the value of a trigonometric function of any
angle ¦È:
1. Determine the function value for the associated reference angle ¦È¡¯.
2. Depending on the quadrant in which ¦È lies, affix the appropriate sign to the function value.
Examples: Find two solutions of the equation. Give your answers in degrees and radians.
1. sin ? ?
1
2
2. csc ? ?
2 3
3
3. tan ? ? 1
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- trigonometric functions of any angle date precalculus
- trigonometric functions of any angle
- 9 3 trigonometric functions of any angle
- r x y z 22 utep
- 4 4 trigonometric functions of any angle
- trig ratios of any angle date period
- 2 trigonometric functions of general angles lies in
- trigonometric functions cpp
- section 5 3 trigonometric functions of any angle
- 13 3 trigonometric functions of any angle