Inverse Trigonometric Functions
Basically...
Inverse Trigonometric Functions are functions that are used to determine the angles, measurements, and missing values of triangles in radians, coordinates, or degrees by methods involving the unit circle, pythagorean theorem, and so on.
Inverse Trigonometric Functions are functions that are used to determine the angles, measurements, and missing values of triangles in radians, coordinates, or degrees by methods involving the unit circle, pythagorean theorem, and so on.
EASY PROBLEMS
How To
A.) Inverse the trigonometric function to the given answer.
Problems
1.) arc sin q = (theta).
Answer: q = sin(theta)
2.) tan-1 s = (theta).
Answer: s = tan (theta)
3.) arc sec f = (theta).
Answer: f = sec (theta).
Problems
1.) arc sin q = (theta).
Answer: q = sin(theta)
2.) tan-1 s = (theta).
Answer: s = tan (theta)
3.) arc sec f = (theta).
Answer: f = sec (theta).
MEDIUM PROBLEMS
How To
A.) y = arc sinx
"Where y = the radian angle whose sin number is x."
B.) Basically
arc__= radians
__radians = coordinates (x or y)
Problems
1.) arc cos 1/2 = ___
cos = x/r
X Value = 1/2
Inverse = unknown
Radian Value = 3.14/3
Answer: cos 3.14/3 = 1/2
2.) sin-1 (sq. root 2)/2
sin = y/r
Y Value = (sq. root 2)/ 2
Inverse = unknown
Radian Value = 3.14/4
Answer: cos 3.14/4 = (sq. root 2)/2
3.) arc tan (sq. root 3)/2
A.) y = arc sinx
"Where y = the radian angle whose sin number is x."
B.) Basically
arc__= radians
__radians = coordinates (x or y)
Problems
1.) arc cos 1/2 = ___
cos = x/r
X Value = 1/2
Inverse = unknown
Radian Value = 3.14/3
Answer: cos 3.14/3 = 1/2
2.) sin-1 (sq. root 2)/2
sin = y/r
Y Value = (sq. root 2)/ 2
Inverse = unknown
Radian Value = 3.14/4
Answer: cos 3.14/4 = (sq. root 2)/2
3.) arc tan (sq. root 3)/2
Hard Problems
How To
A.) Solve for the trigonometric value outside the parenthesis.
Problems
1.) sin (cos-1(1/4))
See Video For Step By Step Process
http://www.youtube.com/watch?v=DEm8jBvXp6s
Answer: cosx = 1/4
2.) cos(tan-1(1))
See Video For Step By Step Process
http://www.youtube.com/watch?v=hBUBKYjjCmw
Answer: cosx = 1(sq. root 2)/ 2
3.) tan(sin-1(2/3))
A.) Solve for the trigonometric value outside the parenthesis.
Problems
1.) sin (cos-1(1/4))
See Video For Step By Step Process
http://www.youtube.com/watch?v=DEm8jBvXp6s
Answer: cosx = 1/4
2.) cos(tan-1(1))
See Video For Step By Step Process
http://www.youtube.com/watch?v=hBUBKYjjCmw
Answer: cosx = 1(sq. root 2)/ 2
3.) tan(sin-1(2/3))
Real World Application Problem
1.) You want to find the slant height of the shadow that your school creates. Your school is 32 ft tall and you are standing 14 ft away from the school where the shadow ends. How far away are your toes to the top of the building?
a.) Draw out scenario
b.) Utilize pythagorean theorem
c.) a^2 + b^2 = c^2
d.) 14^2 + 32^2 = c^2
e.) 1220= c^2
f.) square root of 1220
g.) c = 34.9284
2.) You want to find the angle from you to the top of a flag pole. The angle between the ground and the flag is 90 degrees. The angle between you and the ground is 45 degrees. What is the angle of descent from the top of the flag pole to you?
a.) 90 + 45 = 135
b.) 135 + x = 180
c.) 135 + 45 = 180
d.) Value proven true
e.) x = 45 degrees
3.) A target is 1,000 ft high and 10 miles away. You need to set the elevation angle on your cannon to hit the target; what is the target
a.) Draw out scenario
b.) Utilize pythagorean theorem
c.) a^2 + b^2 = c^2
d.) 14^2 + 32^2 = c^2
e.) 1220= c^2
f.) square root of 1220
g.) c = 34.9284
2.) You want to find the angle from you to the top of a flag pole. The angle between the ground and the flag is 90 degrees. The angle between you and the ground is 45 degrees. What is the angle of descent from the top of the flag pole to you?
a.) 90 + 45 = 135
b.) 135 + x = 180
c.) 135 + 45 = 180
d.) Value proven true
e.) x = 45 degrees
3.) A target is 1,000 ft high and 10 miles away. You need to set the elevation angle on your cannon to hit the target; what is the target
Video
Other Helpful Links
http://www.mathpeer.com/images/trig/unit_circle.gif
http://www.themathpage.com/atrig/inversetrig.htm
http://www.youtube.com/watch?v=sSEb2H8ngEI
http://www.themathpage.com/atrig/inversetrig.htm
http://www.youtube.com/watch?v=sSEb2H8ngEI
Works Cited
Spector, Lawrence. "Trigonometry." The Math Page. 2011. http://www.themathpage.com/atrig/inversetrig.htm. 25 Mar. 2011.
Wesstein, Eric. "Inverse Trigonometric Functions." MathWorld. A Wolfram Web. http://mathworld.wolfram.com/InverseTrigonometricFunctions.html. Mar. 25 2011.
Bourne, M. "Inverse Trig Functions." Interactive Mathematics. http://www.intmath.com/analytic-trigonometry/7-inverse-trigo-functions.php. 25 Mar. 2011.
Larson, Ron and Robert P. Hostetler. Precalculus. New York: Houghton Mifflin Company, 2004.
Authors: Veronica R. and Kaitlyn H., March 25, 2011. Precalculus Presentation.
