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Honors Pre-Calculus > Module 05: > Flashcards

Module 05: Flashcards

1
Q

Find sin θ if cot θ = - 2 and cos θ < 0. (2 points)

A

√5/5

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2
Q

Use basic identities to simplify the expression. (2 points)

cos θ - cos θ sin2θ

  1. sec2θ
  2. sin θ
  3. tan2θ
  4. cos3θ
A

3.cos3θ

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3
Q

Use basic identities to simplify the expression. (2 points)

1/cot2θ+ sec θ cos θ

A

sec2θ

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4
Q

Simplify the expression. (2 points)

(csc2x sec2x)

÷

(sec2 x + csc2x)

  1. sin2x
  2. cos2x
  3. -1
  4. 1
A

4. 1

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5
Q

Factor the algebraic expression below in terms of a single trigonometric function.

csc 2x - 1

A
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6
Q

Find all solutions in the interval [0, 2π).

cos2x + 2 cos x + 1 = 0

A

x = π

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7
Q

Find all solutions in the interval [0, 2π).

(sin x)(cos x) = 0

A

0, π/2; π, 3π/2

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8
Q

Find all solutions to the equation.
cos2x + 2 cos x + 1 = 0

A

cos2x + 2cosx + 1 = 0

(cosx + 1)2 = 0

cosx + 1 = 0

cosx = -1

x = π + 2πn

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9
Q

Find an exact value:

sin(11π/12)

A

(√6 - √2)/4

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10
Q

Find an exact value:

cos (19π/12)

A

(√6 - √2)/4

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11
Q

Write the expression as either the sine, cosine, or tangent of a single angle. (2 points)

sin 48° cos 15° - cos 48° sin 15°

  1. cos 33°
  2. cos 63°
  3. sin 63°
  4. sin 33°
A

4. sin 33°

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12
Q

Write the expression as either the sine, cosine, or tangent of a single angle:

sin (π/2)cos(π/7) + cos(π/2)sin(π/7)

A
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13
Q

Find an exact value. (2 points)

cos 15°

A

√6 +√2

÷

4

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14
Q

Write the expression as either the sine, cosine, or tangent of a single angle. (2 points)

sin 48° cos 15° - cos 48° sin 15°

  1. cos 33°
  2. cos 63°
  3. sin 63°
  4. sin 33°
A

4. sin 33°

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15
Q

Find all solutions to the equation in the interval [0, 2π). (3 points)

cos 4x - cos 2x = 0

A

0, π/3, 2π/3, π, 4π/3, 5π/3

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16
Q

Rewrite with only sin x and cos x. (3 points)

sin 3x

A

2 cos2x sin x + sin x - 2 sin3x

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17
Q

Find the exact value by using a half-angle identity: sin(7π/8)

A
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18
Q

.

Find cot θ if csc θ = √17/4 and tan θ > 0.

A

1/4

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19
Q

Simplify the expression: cot x sin x - sin (π/2 - x) + cos x (1 point)

  1. cos x
  2. sin x
  3. 2 sin x
  4. 2 cos x
20
Q

Find tan θ if sec θ = √37/6 and sin θ < 0

21
Q

Find all solutions in the interval [0, 2π). (1 point)

sec2x - 2 = tan2x

A

No solution

22
Q

Find all solutions to the equation. (1 point)

sin x = √3/2

23
Q

Find an exact value: sin (-11π/12)

A

(√2 - √6)

÷

4

24
Q

Write the expression as the sine, cosine, or tangent of an angle. (1 point)

sin 9x cos x - cos 9x sin x

  1. sin 10x
  2. cos 8x
  3. sin 8x
  4. cos 10x
25
Q

Write the expression as the sine, cosine, or tangent of an angle. (1 point)

cos 112° cos 45° + sin 112° sin 45°

  1. sin 157°
  2. sin 67°
  3. cos 157°
  4. cos 67°
A

4. cos 67°

26
Q

Rewrite with only sin x and cos x. (1 point)

sin 2x - cos 2x

A

2 sinx cosx - 1 + 2 sin2x

27
Q

Find the exact value by using a half-angle identity. (1 point)

sin 22.5°

A

1/2 √(2 - √2)

28
Q

Find all solutions to the equation in the interval [0, 2π). (1 point)

cos x = sin 2x

A

π/6, π/2, 5π/6, 3π/2

29
Q

Rewrite with only sin x and cos x. (1 point)

sin 2x - cos x

  1. 2 sin x cos2x
  2. sin x
  3. cos x (2 sin x - 1)
  4. 2 sin x
A

3. cos x (2 sin x - 1)

30
Q

Verify the identity

31
Q

Find cos θ if sin θ = -12/13 and tan θ > 0

32
Q

Use basic identities to simplify the expression. (6 points)

sin2θ + tan2θ + cos2θ

  1. sec2θ
  2. cos3θ
  3. sin θ
  4. tan2θ
33
Q

Write the expression as the sine, cosine, or tangent of an angle. (6 points)

sin 5x cos x - cos 5x sin x

  1. cos 6x
  2. cos 4x
  3. sin 6x
  4. sin 4x
34
Q

Rewrite with only sin x and cos x. (6 points)

sin 2x - cos 2x

  1. 2 sin2x - 2 sin x cos x + 1
  2. 2 sin x
  3. 2 sin2x + 2 sin x cos x - 1
  4. 2 sin2x - 2 sin x cos x - 1
A

3. 2 sin2x + 2 sin x cos x - 1

35
Q

Verify the identity. (7 points)

cos 4u = cos22u - sin22u

36
Q

Verify the identity.

37
Q

What are the repicrocal identities?

38
Q

What are the quotient identities?

39
Q

What are the Pythagorean identities?

40
Q

What is the confunction identities?

41
Q

What is the Even/Odd Identities?

42
Q

What are the methods for solving trigonometric equations?

A

Step 01: Solve the equations for the trigonometric value

Step 02: Find all solutions, or general solutions, by adding:

  1. 2π n to the radians measures for sine and cosine
  2. πn to radian measures for tangent and cotangent

Step 03: Final all solutions with specific interval by substituting random integers for n.

  1. Accept: solutions within interval
  2. Reject: solutions outside interval

Remember, x-coordinates represent cosine values and y-coordinates represent sine values.

43
Q

What are the sun and different formulas?

44
Q

What are the Multi-Angle Formulas?

45
Q

What are the Half-Angle Formulas?

46
Q

What are the Power Reducing Formula?

Honors Pre-Calculus (5 decks)

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