Triangle Inscribed in a Circle For a triangle inscribed in a circle of radius r. the law of sines ratios a sin A , b sin B , a n d c sin C have value 2 r . The circle in the figure has diameter 1. What are the values of a. b, and c ? (Note: This result provides an alternative way to define the sine function for angles between 0° and 180°. It was used nearly 2000 yr ago by the mathematician Ptolemy to construct one of the earliest trigonometric tables.)
Triangle Inscribed in a Circle For a triangle inscribed in a circle of radius r. the law of sines ratios a sin A , b sin B , a n d c sin C have value 2 r . The circle in the figure has diameter 1. What are the values of a. b, and c ? (Note: This result provides an alternative way to define the sine function for angles between 0° and 180°. It was used nearly 2000 yr ago by the mathematician Ptolemy to construct one of the earliest trigonometric tables.)
Solution Summary: The author explains how to determine the values of a, b, and c in the triangle ABC.
Triangle Inscribed in a Circle For a triangle inscribed in a circle of radius r. the law of sines ratios
a
sin
A
,
b
sin
B
,
a
n
d
c
sin
C
have value 2
r
.
The circle in the figure has diameter 1. What are the values of a. b, and c? (Note: This result provides an alternative way to define the sine function for angles between 0° and 180°. It was used nearly 2000 yr ago by the mathematician Ptolemy to construct one of the earliest trigonometric tables.)
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
Let θ = - 11π/4Part A: What is a coterminal angle of θ such that 0 ≤ θ ≤ 2π?Part B: What are the exact values of all six trigonometric functions evaluated at θ?
Triangle ΔABC has side lengths of a = 15, b equals 15 times square root of 3 and c = 30 inches.
Part A: Determine the measure of angle m∠B.
Part B: Show how to use the unit circle to find tan B.
Part C: Calculate the area of ΔABC.
Part A: Given sinθ = square root of 3/2, determine three possible angles θ on the domain [0,∞).Part B: Given θ = 675°, convert the value of θ to radians and find sec θ.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.
Fundamental Trigonometric Identities: Reciprocal, Quotient, and Pythagorean Identities; Author: Mathispower4u;https://www.youtube.com/watch?v=OmJ5fxyXrfg;License: Standard YouTube License, CC-BY