CHP 6.2 - Inverse Functions
Find the exact value of:
sin[tan-1(4/3)]
sin[tan-1(4/3)] = 4/5
Solve the equation: 2sinΘ + √(2) = 0 on [0,2π).
{5π/4, 7π/4}
What are the 3 Pythagorean Identities?
sin2Θ + cos2Θ = 1
tan2Θ + 1 = sec2Θ
cot2Θ + 1 = csc2Θ
Fin the exact value of cos105*
(√2 - √6)/4
Find the exact value of sin-1(√3/2)
π/3
Find the exact value of:
tan[cos-1(-1/3)]
tan[cos-1(-1/3)] = -2√(2)
Solve the equation: sin(2Θ) = √(3)/2 on [0,2π).
{π/6, π/3, 7π/6, 4π/3}
Which identities are even and which identities are odd?
Even: cosΘ and its reciprocal secΘ
Odd: sinΘ, cscΘ, tanΘ, and cotΘ
Find the exact value of sin π/12
(√6 - √2)/4
Find the exact value of the following composite function:
sin-1(sin π/9)
π/9
Find the exact value of:
csc-12
csc-12 = π/6
Solve the equation: 4sin2Θ - 1 = 0 on [0,2π).
{π/6, 5π/6, 7π/6, 11π/6}
Simplify (cos2Θ-1)/(tanΘcosΘ+tanΘ) by factoring.
= (cosΘ-1)/tanΘ
Find the exact value of sin75*cos15*+cos75*sin15*
1
Find the exact value, if any, of the composite function:
sin[sin-1(-2.5)]
Not defined.
Use a calculator to approximate the expression in radians rounded to two decimal places.
sec-18
sec-18 = 1.45
Solve the equation: 3cos2Θ = sin2Θ on [0,2π).
{π/3, 2π/3, 4π/3, 5π/3}
Establish the identity: [(tanΘ+cotΘ)/(secΘcscΘ)] = 1
Show proof on board.
Find the exact value of sin[cos-1(√3/2)+cot-1(4/3)]
(4+3√3)/10
Find the exact value, if any, of cos-1[cos(-3π/4)]
3π/4
Write tan(sin-1u) as an algebraic expression containing u.
tan(sin-1u) = u/√(1-u2)
Solve the equation: sin2Θ + cosΘ = 3 on [0,2π).
No real solution.
Establish the identity: [1/(1-sinΘ)] + [1/(1+sinΘ)] = 2sec2Θ
Prove on board.
Establish the identity: [cos(a – b)]/(sina*sinb) = (cota*cotb) + 1
Prove on board.
Solve the equation:
12sin-1x=3π
√2/2