Trigonometric FunctionsBrandon Cohen – NWRMS Science Bowl Team Presentation2014-15 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)

1(𝑖𝑛𝑠𝑒𝑟𝑡 𝑠𝑖𝑛 ,𝑐𝑜𝑠 , tan 𝑥)

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

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