logo for solving-math-problems.com
leftimage for solving-math-problems.com

Pre Calculas - Angles in Radians











































how do you find the complementary and supplementary angles, in radians, of 5pi/7

Comments for Pre Calculas - Angles in Radians

Click here to add your own comments

Jan 29, 2012
Pre Calculus - Angles in Radians
by: Staff


Question:

how do you find the complementary and supplementary angles, in radians, of 5pi/7


Answer:

Supplementary angles: when the sum of two angles is 180° (or π radians), those angles are Supplementary angles.

The first letter (“S”) of the word Supplementary stands for a “Straight” line, an angle of 180° (or π radians).

The supplementary angle can also be calculated in RADIANS directly:

Supplementary angle = π - 5π/7

= 7π/7 - 5π/7

= (7π - 5π)/7

= 2π/7

Supplementary angle = 2π/7 radians



Complementary Angles: when the sum of two angles is 90° (or π/2 radians), those angles are Complementary angles.

The first letter (“C”) of the word Complementary stands for “Corner” angle, or 90° (or π/2 radians).

There is no complementary angle to 5π/7 radians, but there is a complementary angle to 2π/7 radians:

The Complementary angle to 2π/7 can also be calculated in RADIANS directly:

Complementary angle = π/2 - 2π/7

= 7π/14 - 4π/14

= (7π - 4π)/14

= (3π)/14

Complementary angle to 2π/7 = 3π/14 radians



Or, if you prefer to work with degrees, the angle of 5π/7 radians can be converted to degrees by setting up a simple proportion:


x/(5π/7) = 180/π

x/(5π/7) = 180/π

[x/(5π/7)] * (5π/7) = (180/π ) * (5π/7)

x * [(5π/7)/(5π/7)] = (180/π ) * (5π/7)

x * [(5π/7)/(5π/7)] = (180 * 5/7) * (π/π)

x * 1 = (180 * 5/7) * 1

x = (180 * 5/7)

x = 128.571° (or 5π/7 radians = 128.571°)


Supplementary angle = 180° - 128.571°

Supplementary angle = 51.429°

The two supplementary angles are: 128.571° and 51.429° (equivalent to 5π/7 and 2π/7 radians)


The Complementary angle to 51.429° can also be calculated as follows:


90° – 51.429° = 38.571° (equivalent to 3π/14 radians)







Thanks for writing.
Staff

www.solving-math-problems.com



Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com