Search results
Results from the WOW.Com Content Network
This equation can have 2, 1, or 0 positive solutions corresponding to the number of possible triangles given the data. It will have two positive solutions if b sin γ < c < b, only one positive solution if c = b sin γ, and no solution if c < b sin γ. These different cases are also explained by the side-side-angle congruence ambiguity.
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, = = =, where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles (see figure 2), while R is the radius of the triangle's circumcircle.
This geometric argument relies on definitions of arc length and area, which act as assumptions, so it is rather a condition imposed in construction of trigonometric functions than a provable property. [2] For the sine function, we can handle other values. If θ > π /2, then θ > 1. But sin θ ≤ 1 (because of the Pythagorean identity), so sin ...
We denote further D = c / b sin β (the equation's right side). There are four possible cases: If D > 1, no such triangle exists because the side b does not reach line BC. For the same reason a solution does not exist if the angle β ≥ 90° and b ≤ c. If D = 1, a unique solution exists: γ = 90°, i.e., the triangle is right-angled.
Sine and cosine are each other's cofunctions. In mathematics, a function f is cofunction of a function g if f(A) = g(B) whenever A and B are complementary angles (pairs that sum to one right angle). [1] This definition typically applies to trigonometric functions. [2] [3] The prefix "co-" can be found already in Edmund Gunter's Canon ...
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
Given two sides a and b and the angle between the sides C, the area of the triangle is given by half the product of the lengths of two sides and the sine of the angle between the two sides: [85] Area = Δ = 1 2 a b sin C {\displaystyle {\mbox{Area}}=\Delta ={\frac {1}{2}}ab\sin C}