Answer:
Option B. Cosec θ = –5/3
Option C. Cot θ = 4/3
Option D. Cos θ = –4/5
Step-by-step explanation:
From the question given above, the following data were obtained:
Tan θ = 3/4
θ is in 3rd quadrant
Recall
Tan θ = Opposite / Adjacent
Tan θ = 3/4 = Opposite / Adjacent
Thus,
Opposite = 3
Adjacent = 4
Next, we shall determine the Hypothenus. This can be obtained as follow:
Opposite = 3
Adjacent = 4
Hypothenus =?
Hypo² = Opp² + Adj²
Hypo² = 3² + 4²
Hypo² = 9 + 16
Hypo² = 25
Take the square root of both side
Hypo = √25
Hypothenus = 5
Recall:
In the 3rd quadant, only Tan is positive.
Therefore,
Hypothenus = –5
Finally, we shall determine Sine θ, Cos θ, Cot θ and Cosec θ to determine which option is correct. This can be obtained as follow:
Opposite = 3
Adjacent = 4
Hypothenus = –5
Sine θ = Opposite / Hypothenus
Sine θ = 3/–5
Sine θ = –3/5
Cos θ = Adjacent / Hypothenus
Cos θ = 4/–5
Cos θ = –4/5
Cot θ = 1/ Tan θ
Tan θ = 3/4
Cot θ = 1 ÷ 3/4
Invert
Cot θ = 1 × 4/3
Cot θ = 4/3
Cosec θ = 1/ Sine θ
Sine θ = –3/5
Cosec θ = 1 ÷ –3/5
Invert
Cosec θ = 1 × –5/3
Cosec θ = –5/3
SUMMARY
Sine θ = –3/5
Cos θ = –4/5
Tan θ = 3/4
Cot θ = 4/3
Cosec θ = –5/3
Therefore, option B, C and D gives the correct answer to the question.
Answer:
Distribution, equal groups, skip counting, repeated addition, and array.
Step-by-step explanation:
Answer:
6a) x = -6
Let's solve your equation step-by-step.
14= 2x + 26
Step 1: Flip the equation.
2x + 26 = 14
Step 2: Subtract 26 from both sides.
2x + 26 − 26 = 14 − 26
2x = −12
Step 3: Divide both sides by 2.
2x/2 = −12/2
x=−6
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7a) x = 4.25
Let's solve your equation step-by-step.
−30 =4 − 8x
Step 1: Simplify both sides of the equation.
−30 = 4 − 8x
−30 = 4 + −8x
−30 = −8x + 4
Step 2: Flip the equation.
−8x + 4 = −30
Step 3: Subtract 4 from both sides.
−8x + 4 − 4 = −30 − 4
−8x = −34
x=17/4 (Decimal: 4.25)
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8a) x = 8
Let's solve your equation step-by-step.
3(x − 4) = 12
Step 1: Simplify both sides of the equation.
3(x − 4) = 12
(3)(x) + (3)(−4)= 12(Distribute)
3x + −12 = 12
3x − 12= 12
Step 2: Add 12 to both sides.
3x − 12 +1 2 = 12 + 12
3x = 24
Step 3: Divide both sides by 3.
3x/3=24/3
x=8
Answer:
90
Step-by-step explanation:
