PreCalc Chapter 7

cos(α+β )=cosαcosβ______sinαsinβ

-

sin(α-β )=sinαcosβ______sinβcosα

-

tan^2Θ-sec^2Θ=____

-1

cos(-Θ)-cosΘ=_____

0

sin^2(Θ/2)=_____/2

1-cosΘ

It is impossible to obtain exact values for the inverse secant function

False

The domain of y=sin-1x is -π/2≤x≤π/2

False

sin(sin-1(0)) and cos(cos-1(0))=0

True

y=tan-1x means x=tany, where -∞<x<∞ and -π/2≤x≤π/2

True

In establishing an identity, it is often easiest to just multiply both sides by a well-chosen nonzero expression involving the variable

false

Most trigonometric equations have unique solutioms

false

cos(π/2-Θ)=cosΘ

false

sin(2Θ) has two equivalent forms

false

sin(α+β )=sinα+sinβ+2sinαsinβ

false

tan(2Θ)+tan(2Θ)=tan(4Θ)

false

tan75°=tan30°+tan45°

false

the euqation sinΘ=2 has a real solutio theat can be found using a calculator

false

suppose that f and g are two functions with the same domain. If f(x)=g(x) for every x in the fomain, the equation is called an _________. Otherwise, it is called a ________ equation.

identity; conditional

The value of sin-1[sinπ/2] is ______

pi/2

cos-1[cosπ/5]=______

pi/5

all the solutions to the equation sinΘ=1/2 are _________

pi/6+2kpi; 5pi/6+2kpi (kEi)

two solutions of the equation sinΘ=1/2 are_____ and _______

pi/6; 5pi/6

cos(2Θ)=cos^2(Θ)-_______= _____-1= 1-_________

sin^2(Θ); 2cos^2(Θ); 2sin^2(Θ)

tan^2(Θ/2)=1-cosΘ/_____

sinΘ

cos(tan-1(1))

square root 2/2

cos(2Θ) has three equivalent forms

true

csc-1(0.5) is not defined

true

sin(-Θ)+sinΘ=0 for any value of Θ

true

tanΘxcosΘ=sinΘ for any Θ≠(2k+1)π/2

true

the domain of the inverse cotangent function is the set of real numbers

true

y=sec-1x means ________, where |x|≥______ and ____≤y≤_____, y≠π/2

x=secy; 1; 0; pi

y = sin-1x means that __________ where -1≤x≤1 and -π/2≤x≤π/2

x=siny