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Created by T. Madas Created by T. Madas 9. sin 3cos 2sin 3 3 x x x π π + − + ≡ (**) 10. cos 3sin 2cos 3 3 x x x π π
Recall the definitions of the trigonometric functions by means of the unit circle, x2 + y2 = 1. Three more functions are defined in terms of these, secant (sec), cosecant (cosec or csc) and cotangent (cot). (3) The functions cos and sin are the basic ones.
In this unit we are going to look at trigonometric identities and how to use them to solve trigonometric equations. A trigonometric equation is an equation that involves a trigonometric function or functions.
Objectives. After studying this chapter you should. be able to handle with confidence a wide range of trigonometric identities; be able to express linear combinations of sine and cosine in any of the forms Rsin ( q – a ) or Rcos ( q – a ); know how to find general solutions of trigonometric equations;
Trigonometric Identities Worksheet. I. Prove each identity. 1) tanxcos x =sinx. x . ' tan x. 5) Slnx=- secx. II. Prove each identity. 1) esc x(l + sin x) == 1+ esc x. 3) coscx(secx-1)=1-cosx. 1- tan x. 5) =-tanx . 1- cotx . III. Prove each identity. 2 . sin x + 1. 1) sm x tan x + sec x ==--- cosx . ) 1+ si. 1- x esc x-I. l+sinx . .
Fundamental trig identity. cos(. (cos x)2 + (sin x)2 = 1. 1 + (tan x)2 = (sec x)2 (cot x)2 + 1 = (cosec x)2.
Introduction to the Trigonometric Ratios. To help using the. SIN = OPPOSITE. COS = ADJACENT. TAN = OPPOSITE. Solving for a Side Within a Right Triangle Using the. Trigonometric Ratios. 1: Determine which trigonometric ratio to use. 2: Create an equation using the trig ratio sine and then solve for the unknown .
