Fundamental trig identity (cosx)2 +(sinx)2 = 1 1+(tanx)2 = (secx)2 (cotx)2 +1 = (cosecx)2 Odd and even properties cos( x) = cos(x) sin( x) = sin(x) tan( x) = tan(x) Double angle formulas sin(2x) = 2sinxcosx cos(2x) = (cosx)2 (sinx)2 cos(2x) = 2(cosx)2 1 cos(2x) = 1 2(sinx)2 Half angle formulas sin(1 2 x) 2 = 1 2 (1 cosx)

List of trigonometric identities 2 Trigonometric functions The primary trigonometric functions are the sine and cosine of an angle. These are sometimes abbreviated sin(θ) and cos(θ), respectively, where θ is the angle, but the parentheses around the …

This unit is designed to help you learn, or revise, trigonometric identities. You need to know these identities, and be able to use them confidently. They are used in many different branches of mathematics, including integration, complex numbers and mechanics. The best way to learn these identities is to have lots of practice in using them. So we

Math Formulas: Trigonometry Identities Right-Triangle De nitions 1. sin = Opposite Hypotenuse 2. cos = Adjacent Hypotenuse 3. tan = Opposite Adjacent 4. csc = 1 sin = Hypotenuse Opposite 5. sec = 1 cos = Hypotenuse Adjacent 6. cot = 1 tan = Adjacent Opposite Reduction Formulas 7. sin( x) = sin(x) 8. cos( x) = cos(x) 9. sin ˇ 2 x = cos(x) 10 ...

Trigonometric Identities . MVCC Learning Commons IT129 . Six Trigonometric Functions . Right triangle definitions, where : 0 < 𝜃𝜃< 𝜋𝜋/2: sin: 𝜃𝜃= opp hyp csc 𝜃𝜃= hyp opp cos𝜃𝜃= adj hyp sec𝜃𝜃= hyp adj tan 𝜃𝜃= opp adj cot𝜃𝜃= adj opp: Circular function definitions, where :

Trigonometric Identities Cheat Sheet Quotient Identities tan = sin cos cot = cos sin Reciprocal Identities sin = 1 csc cos = 1 sec tan = 1 cot Co-function Identities sin = cos 2 cos = sin 2 tan = cot 2 csc = sec 2 sec = csc 2 cot = tan 2 Phytagorean Identities sin2 cos2 = 1 1 tan2 = sec2 1 cot2 = csc2 Double Angle Identities

Use reciprocal, quotient, Pythagorean, symmetry, and opposite-angle identities. (Lesson 7-1) Verify trigonometric identities. (Lessons 7-2, 7-3, 7-4) Use sum, difference, double-angle, and half-angle identities. (Lessons 7-3, 7-4) Solve trigonometric equations and inequalities. (Lesson 7-5) Write a linear equation in normal form. (Lesson 7-6)

Table of Trigonometric Identities Prepared by Yun Yoo 1. Pythagorean Identities sin2 x+cos2 x = 1 1+tan2 x = sec2 x 1+cot2 x = csc2 x 2. Reciprocal identities cscx = 1 sinx secx = 1 cosx cotx = 1 tanx sinx = 1 cscx cosx = 1 secx tanx = 1 cotx 3. Quotient Identities tanx = sinx cosx cotx = cosx sinx 4. Co-Function Identities sin(… 2 ¡x ...

Trigonometric Identities sin 2x +cos x =1 1+tan 2x = sec x 1+cot 2x = csc x sin x =cos(90−x) =sin(180−x) cosx =sin(90−x) = −cos(180−x) tan x =cot(90−x) = −tan(180−x) Angle-sum and angle-difference formulas sin(a ± b) =sinacosb± cosasinbcos(a ± b) =cosacosbmsinasinbtan( ) tan tan tan tan a b a b a b ± = ± 1m cot( ) cot cot

A trigonometric identity is a relation between trigonometric expressions which is true for all values of the variables (usually angles). There are a very large number of such identities. In this Section we discuss only the most important and widely used.