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Trigonometric Identities Worksheet - Assignment | MAT 170, Assignments of Pre-Calculus

Arizona State University (ASU) - TempePre-Calculus

Material Type: Assignment; Class: Precalculus; Subject: Mathematics; University: Arizona State University - Tempe; Term: Unknown 1989;

Typology: Assignments

Pre 2010

Uploaded on 09/02/2009

koofers-user-wpj
koofers-user-wpj 🇺🇸

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TrigonometricIdentitiesWorksheet.
There are numerous trig identities, many of them very basic. You should know these
sincetheyappearfrequently:
)sin(cos),cos(sin
22
ππ
+=−= xxxx horizontalshifts.
sin(-x)=-sinx,cos(-x)=cosx,tan(-x)=-tanxsymmetries.
xxxxxx
222222
cos1sin,sin1cos,1cossin −=−==+ pythagoreanidentities.
xxxxxx cossin2)2sin(,sincos)2cos(
22
=−= doubleangleidentities.
Useanyappropriatemethodstoprovethefollowingidentities.
1.
x
x
xcos
tan
sin =
2.
x
x
x
x
x
x
cos
sin
1
sin
cos
cos
sin =+
3. xx
2
sin21)2cos( −=
4. x
x
xx cos
cos
1
tansin −=
Completelysolveforxoverthegivenintervals.
5. 2cos
2
x+cosx-1=0,0≤x≤2π
6. cos(2x)=cosx,0≤x≤2π

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Trigonometric Identities Worksheet.

There are numerous trig identities, many of them very basic. You should know these

since they appear frequently:

sin cos( 2 ), cos sin( 2 ) π π x = x − x = x + horizontal shifts.

sin (- x ) = -sin x , cos (- x ) = cos x , tan (- x ) = -tan x symmetries.

x x x x x x

2 2 2 2 2 2 sin + cos = 1 , cos = 1 −sin , sin = 1 −cos pythagorean identities.

cos( 2 x ) cos x sin x , sin( 2 x ) 2 sin x cos x

2 2 = − = double angle identities.

Use any appropriate methods to prove the following identities.

  1. x x

x cos tan

sin

x x x

x

x

x

sin cos

sin

cos

cos

sin

  • =
  1. x x

2 cos( 2 )= 1 − 2 sin

  1. x x

x x cos cos

sin tan = −

Completely solve for x over the given intervals.

  1. 2cos

2 x + cos x - 1 = 0, 0 ≤ x ≤ 2 π

  1. cos (2 x ) = cos x , 0 ≤ x ≤ 2 π