5.1
5.2
5.3
5.4
5.5
100
Simplify the Trig Expression:
tan(θ)cos(θ)
sin(θ)
100
(1 + cosx)/(sinx) = cscx + cotx
(1 + cosx)/(sinx) =
(1/sinx) + (cosx/sinx) =
cscx + cotx
100
Solve the Equation on the interval [0,2π)
2cos2θ = sinθ + 1
π, π/6, 3π/2
100
Simplify Sin(105°) using a Sum and Difference Formula
What is (√6 + √2)/4 ?
100
cosθ = -7/11 where π<θ<π/2, find sin2θ.
(84√2)/121
200
sin(θ)csc(θ) - sin2(θ)
cos2(θ)
200
Verify the Trig Identity:
cosx(tan2x + 1) = sec(x)
cosx(tan2x + 1)
cosx(sec2x)
cosx(1/cos2x)
1/cosx
sec(x)
200
Solve the equation over the interval [0,2π)
4sin2(3θ) - 3 = 0
π/9, 2π/9, 4π/9, 5π/9
200
Simplify cos(15°) using a Sum and Difference Formula.
What is (√6 + √2)/4 ?
200
Rewrite cos5xsin4x as a sum or difference.
1/2(sin9x - sinx)
300
Simplify the Trig Expression:
(secθ/cscθ) + (sinθ/cosθ)
2tanθ
300
(1 - tan2x)/(1 + tan2x) = 1-2sin2x
(1 - tan2x)/(1 + tan2x) =
(1 - tan2x)/(sec2x) =
(1 / sec2x) - (tan2x/sec2x) =
cos2x - sin2x =
(1 - sin2x) - sin2x =
1 - 2sin2x
300
Solve the equation and give the general solution:
4cosx = 1 + 2cosx
π/3 = 2πn, 5π/3 + 2πn
where n is an integer
300
Simplify Cos(95°)Cos(55°)-Sin(95°)Sin(55°).
What is -√3/2 ?
300
Find the Sin(75°) using a half angle formula.
400
(sin4x - cos4x) / (sin2x - cos2x)
1
400
Verify the Trig Identity:
(sinx + cosx)2 + (sinx - cosx)2 = 2
(sinx + cosx)2 + (sinx - cosx)2
sin2x + 2cosxsinx + cos2x + sin2x - 2cosxsinx + cos2x
2sin2x + 2cos2x
2(sin2x + cos2x)
2(1)
2
400
Solve the equation over the interval [0,2π)
3tan4x- 10tan2x = -3
π/6, 5π/6, 7π/6, 11π/6, π/3, 2π/3, 4π/3, 5π/3
400
Simplify tan(255°) using a sum and difference formula.
What is 2 + √3 ?
400
Find the exact value of cos 195° + cos 125° using a sum to product formula.
-√6/2
500
Simplify the Trig Expression:
sec(-x) + tan(-x)cos(𝝅/2 - x)
cos(x)
500
Verify the Trig Identity:
(1/(sinx - 1)) - (1/(sinx + 1)) = -2sec2x
(1/(sinx - 1)) - (1/(sinx + 1)) =
(sinx + 1 - sinx + 1)/(sin2x -1) =
2/(-cos2x) =
-2sec2x
500
Solve the equation and give the general solution:
2sin(3x) - √2 = 0
π/12 + (2πn)/3, π/4 + (2πn)/3
Where n is an integer
500
cos 𝛼 = 8/17 and tan 𝛽 = 5/12 , the cos (𝛼 + 𝛽) is equal to...
What is 21/221 ?
500
Rewrite cos4x as a sum of first powers (rewrite this using the power reducing formula then simplify).
1/4(1 + 2cos2x +(1 + cos4x)/2)