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

2. 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)

3. 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)

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

5. 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.

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

7. 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

9. Right Triangle Trigonometry & Circular Functions Practice Problems

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