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:the 1 or 4
Step-by-step explanation:
Answers:
- x = 4
- angle CAB = 26 degrees
- angle ABC = 24 degrees
Depending on your teacher, you may or may not have to input the word "degrees" or the degree symbol.
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Explanation:
We use the remote interior angle theorem.
This says to add two interior angles, and the sum is equal to the exterior angle that is not adjacent to any of the interior ones. Hence the "remote".
(angle CAB) + (angle ABC) = exterior angle
(6x+2) + (9x-12) = 50
15x-10 = 50
15x = 50+10
15x = 60
x = 60/15
x = 4 is the first answer
We can then find the interior angles
angle CAB = 6x+2 = 6(4)+2 = 24+2 = 26 degrees is the second answer
angle ABC = 9x-12 = 9(4)-12 = 36-12 = 24 degrees is the third answer
Then notice how 26+24 = 50 to help confirm the answers.
Answer:
Step-by-step explanation:
See completed figure attached.
Note that some blanks are missing colours from the question.
