Trigonometric Functions Brandon Cohen NWRMS Science Bowl Team

Trigonometric Functions Brandon Cohen – NWRMS Science Bowl Team Presentation 2014 -15 Season

Introduction § Also referred to as a “circular function” § Trig Functions are the relations of an angle (relation of angle of triangle to the lengths of its sides) § In the real world? § § Study of Triangles (Compute unknown) Periodic Phenomena (sound/light waves) “Elementary” Physics (Resolve vectors) Other Applications (Modeling with Weather)

Common Trigonometric Functions § Most familiar trigonometric functions are: § Sine (sin) § Cosine (cos) § Tangent (tan) § Commonly defined as ratios of two sides of a triangle containing the angle (equivalently defined as lengths of these line segments)

Application of Knowledge (SOH, CAH, TOA) NOT TO WORRY ABOUT THESE. . YET

Reciprocal Functions § ONLY 3 Remaining Functions § Cosecant (csc) is reciprocal of sine § Secant (sec) is reciprocal of cosine § Cotangent (cot) is reciprocal of tangent § The ratio of these functions is simply the reciprocal of their accompanying trigonometric function.

Application of Knowledge (Reciprocal Trig Functions) GENERALIZED RECIPROCAL RULE?

The Unit Circle and Trigonometric Functions § A circle with radius 1 that is centered at the origin § Measures common angles and their results § Positive angles & measurements in counterclockwise/Negative in clockwise § Useful for providing quick and reliable calculations § (Other angles may be formed from these common angles and their results using the trigonometric identities, but in most cases it would be quicker to use a calculator for those values!) § COORDINATES ARE (COS value, SIN value). . the other 4 can be found using these 2

Right Triangle Trigonometry & Circular Functions Practice Problems

A sin(θ) = cos(θ) = 8 tan(θ) = 6 Can we find the reciprocals? Yes, we can! csc(θ) = B θ 4 C sec(θ) = cot(θ) =