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.
Let distance be s and velocity be v
s = 5t⁴ - 10t² + 6
We know velocity is the change in distance per unit time, so
v = ds/dt
v = 20t³ - 20t
The area of triangle formula is A = B*H / 2
so it means 16 square = (<span>x+4) x /2
so x²+4x -32=0, D' = 2²- (-32)= 36, sqrt of D' = 6
so x = -2 -6 = -8 or x= -2 +6 = 4
x must be positive so x = 4</span>
Answer:
2x + 15= 33
Step-by-step explanation:
Jerry started doing sit-ups every day. The first day he did 17 sit-ups. Every day after that he did 4 more sit-ups than he had done the previous day. Today Jerry did 73 sit-ups. Write an equation that could be solved to find the number of days Jerry has been doing sit-ups, not counting the first day. Let n represent the number of days.
