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Marianna [84]
3 years ago
6

Consider angle θ in Quadrant ll, where cos θ= -12/13. what's the value of sin θ​

Mathematics
1 answer:
IgorLugansk [536]3 years ago
8 0

Answer:

5/13

Step-by-step explanation:

According to SOH CAH TOA

cos theta = adj/hyp = -12/13

Get the opposite using pythagoras  theorem

13^2 = (-12)^2 + opp^2

169 = 144 + opp^2

opp^2 = 169-144

opp^2 = 25

opp = 5

Get sin θ​

sin θ​ = opp/hyp

sin θ​ = 5/13

hence the value of  sin θ​ is 5/13

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Answer:

D. <em>a</em> = 11.71 and <em>b</em> = 15.56

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

<u>Trigonometry</u>

  • All angles in a triangle add up to 180°

<u>Pre-Calculus</u>

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AC = b

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<u>Step 2: Find missing ∠</u>

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  2. Combine like terms:              m∠C + 115° = 180°
  3. Isolate unknown:                   m∠C = 25°

<u>Step 3: Find measure of </u><em><u>b</u></em>

  1. Substitute:                    \frac{sin(25)}{7} =\frac{sin(110)}{b}
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  3. Isolate <em>b</em>:                       b=\frac{7sin(110)}{sin(25)}
  4. Evaluate:                       b=15.5645
  5. Round:                          b \approx 15.56

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  1. Substitute:                    \frac{sin(25)}{7} =\frac{sin(45)}{a}
  2. Cross-multiply:             asin(25)=7sin(45)
  3. Isolate <em>a</em>:                       a=\frac{7sin(45)}{sin(25)}
  4. Evaluate:                       a=11.7121
  5. Round:                          a \approx 11.71
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