Chapter 3
... Solution: m6 1 = 47◦ because they are vertical angles. Because the lines are parallel, m6 3 = 47◦ by the Corresponding Angles Theorem. Therefore, m6 2 = 47◦ . 1 and 6 3 are alternate exterior angles. Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the alternat ...
... Solution: m6 1 = 47◦ because they are vertical angles. Because the lines are parallel, m6 3 = 47◦ by the Corresponding Angles Theorem. Therefore, m6 2 = 47◦ . 1 and 6 3 are alternate exterior angles. Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the alternat ...
CK-12 Trigonometry
... The domain of this function is the set of x values {2,3,5} The variable x is often referred to as the independent variable, while the variable y is referred to as the dependent variable. We talk about x and y this way because the y values of a function depend on what the x values are. That is why we ...
... The domain of this function is the set of x values {2,3,5} The variable x is often referred to as the independent variable, while the variable y is referred to as the dependent variable. We talk about x and y this way because the y values of a function depend on what the x values are. That is why we ...
Deriving Trig Identities (Word Document)
... When “solving a triangle,” you are expected to find the lengths of all its sides and the measures of all its angles. Previously, we have been able to solve only RIGHT triangles. Not all triangles are right triangles. What about oblique triangles? We can solve ANY triangle, right or oblique, if we kn ...
... When “solving a triangle,” you are expected to find the lengths of all its sides and the measures of all its angles. Previously, we have been able to solve only RIGHT triangles. Not all triangles are right triangles. What about oblique triangles? We can solve ANY triangle, right or oblique, if we kn ...
Pants decompositions of random surfaces
... (To define a “random” hyperbolic surface we need a probability measure on the moduli space of hyperbolic metrics. We use the renormalized Weil-Petersson volume form. We discuss this notion of randomness more below.) As another piece of context for our result, we mention the analogous questions for h ...
... (To define a “random” hyperbolic surface we need a probability measure on the moduli space of hyperbolic metrics. We use the renormalized Weil-Petersson volume form. We discuss this notion of randomness more below.) As another piece of context for our result, we mention the analogous questions for h ...
θ + - mrseehafer
... magnitudes of the rotations that map (1, 0) onto these points are θ (for P at the right), –θ (for Q), 180º + θ (for H ), and 180º - θ (for J ). So the sines and cosines of these magnitudes are either equal or opposites. ...
... magnitudes of the rotations that map (1, 0) onto these points are θ (for P at the right), –θ (for Q), 180º + θ (for H ), and 180º - θ (for J ). So the sines and cosines of these magnitudes are either equal or opposites. ...
