Trigonometry exam 1 preparation

1. 1An [blank_start]angle[blank_end] is formed by 2 rays with a common starting point.

   1. Aangle
2. 2a [blank_start]ray[blank_end] is a line with only one endpoint.

   1. Aray
3. 3Angles are measured using [blank_start]degrees, Radians, gradians[blank_end], and [blank_start]revolutions[blank_end]. [blank_start]Degrees[blank_end] 1/360th of a revolution. [blank_start]Radians[blank_end] are a unit of measurement based on the radius. 1 revolution = [blank_start]2[blank_end]π. [blank_start]Gradians[blank_end] are 1/400th of a revolution. A [blank_start]revolution[blank_end] is just a full circle.

   1. Adegrees, Radians, gradians
   2. Brevolutions
   3. CDegrees
   4. DRadians
   5. EGradians
   6. Frevolution
   7. G2
4. 4Converting between [blank_start]radians and degrees[blank_end] and vice versa.
   x [blank_start]radians[blank_end] = (180°*x)/π [blank_start]radians[blank_end] = x°
   x° = (x*π [blank_start]radians[blank_end])/180° = [blank_start]x radians[blank_end].

   1. Aradians
   2. Bradians
   3. Cx radians
   4. Dradians
   5. Eradians and degrees
5. 5[blank_start]Complementary[blank_end] angles add up to 90°

   1. AComplementary
6. 6[blank_start]Supplementary[blank_end] angles add up to 180°

   1. ASupplementary
7. 7The standard position is having the [blank_start]initial side on the x-axis[blank_end]. The [blank_start]initial side[blank_end] is the fixed side of the angle. The [blank_start]terminal side[blank_end] is the moving side that ends the angle.

   1. Ainitial side on the x-axis
   2. Binitial side
   3. Cterminal side
8. 8[blank_start]Directionality[blank_end] determines whether something is positive or negative. [blank_start]Counterclockwise[blank_end] is positive. [blank_start]Clockwise[blank_end] is negative.

   1. ADirectionality
   2. BCounterclockwise
   3. CClockwise
9. 9[blank_start]Co-terminal angles[blank_end] are 2 angles that have the same terminal side. They subtract to form a multiple of [blank_start]360[blank_end]°, [blank_start]400[blank_end] gradians, [blank_start]2[blank_end]π radians or [blank_start]1[blank_end] revolution.

   1. ACo-terminal angles
   2. B360
   3. C400
   4. D1
   5. E2
10. 10The biggest side ([blank_start]hypotenuse[blank_end]) is [blank_start]opposite[blank_end] the biggest angle. The [blank_start]opposite[blank_end] is [blank_start]opposite[blank_end] the angle we are starting from and [blank_start]Adjacent[blank_end] is [blank_start]adjacent[blank_end] to our starting angle.

    1. Ahypotenuse
    2. Bopposite
    3. Copposite
    4. Dopposite
    5. EAdjacent
    6. Fadjacent

11. 11When estimating roots, you find the nearest 2 square roots, use the lower one as your starting point ([blank_start]X[blank_end]), and the difference between the lesser and greater squares([blank_start]Y[blank_end]) divided by the difference between the two closest square roots (1 higher, 1 lower)[[blank_start]z[blank_end]]. [blank_start]X[blank_end] +[blank_start]y/z[blank_end].

    1. AX
    2. BX
    3. Cy/z
    4. DY
    5. Ez
12. 12Triangles have [blank_start]180[blank_end]°

    1. A180
13. 13[blank_start]Similar[blank_end] shapes have the same [blank_start]angles[blank_end] and have [blank_start]sides[blank_end] proportional to each other.

    1. ASimilar
    2. Bangles
    3. Csides
14. 14[blank_start]sine(x)^-1[blank_end] ≠ 1/sine(x) [blank_start]=[blank_end] (sinex)^-1

    1. Asine(x)^-1
    2. B=
15. 15A [blank_start]unit circle[blank_end] is a circle with a radius of 1 and the formula of x^2 + y^2 = 1. You predict points on the [blank_start]unit circle[blank_end] using a [blank_start]right triangle[blank_end], and writing it as ([blank_start]Cosine[blank_end] X, [blank_start]Sine[blank_end] X). When using an angle, it should be the one centered at the [blank_start]center[blank_end]. The 90° of the right triangle should be [blank_start]directly under[blank_end] the point you're trying to find.

    1. Aunit circle
    2. Bunit circle
    3. Cright triangle
    4. DCosine
    5. ESine
    6. Fcenter
    7. Gdirectly under
16. 16What is this and what should I memorize?

    

    1. AA unit circle
    2. BA revolution marked in degrees.
    3. CMemorize these points. From 0°-90°
    4. DMemorize the degrees.
17. 17[blank_start]Radians[blank_end] are unmarked numbers and [blank_start]Degrees/Gradians[blank_end] are marked with "°"

    1. ADegrees/Gradians
    2. BRadians
18. 18[blank_start]30[blank_end]°=π[blank_start]/6[blank_end]. If this has an even numerator (an even number attached to the π), it simplifies down to [blank_start]60[blank_end]°, or π[blank_start]/3[blank_end].

    1. A/6
    2. B/3
    3. C60
    4. D30
19. 19[blank_start]45[blank_end]° = π[blank_start]/4[blank_end]

    1. A45
    2. B/4
20. 20[blank_start]Cos[blank_end] X = x/1. [blank_start]Sin[blank_end] X = y/1. [blank_start]Tan[blank_end] X = y/x, or the ratio of [blank_start]sine[blank_end] to [blank_start]cosine[blank_end].

    1. ACos
    2. BSin
    3. CTan
    4. Dsine
    5. Ecosine
21. 21[blank_start]Sec[blank_end] X = 1/x or 1/[blank_start]cos[blank_end] X. [blank_start]csc[blank_end] X = 1/y or 1/[blank_start]sin[blank_end] X. [blank_start]Cot[blank_end] X = x/y = [blank_start]Cos[blank_end] X/ [blank_start]Sin[blank_end] X.

    1. ASec
    2. Bcos
    3. Ccsc
    4. Dsin
    5. ECot
    6. FCos
    7. GSin
22. 22[blank_start]sin[blank_end] X = y/1. [blank_start]Cos[blank_end] X = x/1. The [blank_start]unit circle formula[blank_end] is (cos X)^2 + (sin X)^2 = 1 when substituting [blank_start]X[blank_end] and [blank_start]Y[blank_end] for their trigonometric equivalents.

    1. Asin
    2. BCos
    3. Cunit circle formula
    4. DX
    5. EY
23. 23[blank_start]Tan, Sin, Cos[blank_end] <1 or >-1.

    1. ATan, Sin, Cos
24. 24[blank_start]Cot, csc, sec[blank_end] >1 or <-1

    1. ACot, csc, sec
25. 25[blank_start]conditional equation[blank_end]- sometimes is true. [blank_start]Identity equation[blank_end]- always true

    1. Aconditional equation
    2. BIdentity equation
26. 26Cos X = [blank_start]Adjacent/Hypotenuse[blank_end]
    Sin X = [blank_start]Opposite/Hypotenuse[blank_end]
    Tan X = [blank_start]Opposite/Adjacent[blank_end]
    Sec X = [blank_start]Hypotenuse/Adjacent[blank_end]
    Csc X = [blank_start]Hypotenuse/Opposite[blank_end]
    Cot X = [blank_start]Adjacent/Opposite.[blank_end]

    1. AAdjacent/Hypotenuse
    2. BOpposite/Hypotenuse
    3. COpposite/Adjacent
    4. DHypotenuse/Adjacent
    5. EHypotenuse/Opposite
    6. FAdjacent/Opposite.
27. 27zeroes [blank_start]can't[blank_end] be canceled

    1. Acan't
28. 28Reciprocal identities:
    [blank_start]Sec = 1/Cos[blank_end], [blank_start]Csc = 1/Sin[blank_end], [blank_start]Cot = 1/tan[blank_end] [blank_start]Cos = 1/sec[blank_end], [blank_start]Sin = 1/csc[blank_end], [blank_start]Tan = 1/Cot[blank_end].
    Pythagorean Identities:
    [blank_start]sin^2 + cos^2 = 1[blank_end] [blank_start]tan^2 +1 = sec^2[blank_end] [blank_start]1+Cot^2 = Csc^2[blank_end]

    1. ASec = 1/Cos
    2. BCsc = 1/Sin
    3. CCot = 1/tan
    4. DCos = 1/sec
    5. ESin = 1/csc
    6. FTan = 1/Cot
    7. Gsin^2 + cos^2 = 1
    8. Htan^2 +1 = sec^2
    9. I1+Cot^2 = Csc^2
29. 29There are two rules when making something an identity/proving it's an identity function. One-[blank_start]nothing can swap sides[blank_end], they [blank_start]must[blank_end] stay on their respective sides. Two- don't mess with [blank_start]both sides[blank_end] of the equation at the same time. (Ex: Squaring)

    1. Anothing can swap sides
    2. Bswapping sides is ok
    3. Cmust
    4. Ddon't have to
    5. Eboth sides
    6. Fone side
30. 30f^-1 is the [blank_start]inverse[blank_end]. (f(x))^-1 is [blank_start]1/f(x)[blank_end]

    1. Ainverse
    2. B1/f(x)
31. 31A handy tip is to convert things to just Sine and Cosine first.

    1. ATrue
    2. BFalse

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N/A Old stuff Quiz on Trigonometry exam 1 preparation, created by Nathaniel Parkinson on 19/01/2021.

Author

Nathaniel Parkinson

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