If A= arcsin(-4/5) in Quadrant IV and B=arctan(5/12) in Quadrant III, what is the values of tan(arcsin(-4/5)+arctan(5/12))? ASAP please...
Answers
Answer:
-33/56
Step-by-step explanation:
suppose: A,B are the 2 angles of a triangle
we have: A = arcsin[tex]\frac{-4}{5}[/tex]
B = arctan [tex]\frac{5}{12}[/tex]
=> sin A = [tex]\frac{-4}{5}[/tex] => cos A = [tex]\sqrt{1-\frac{(-4)^{2} }{5^{2} } } =\frac{3}{5}[/tex] (because A is in quadrant IV)
tan B = [tex]\frac{5}{12}[/tex]
have:
[tex]1+ cot^{2}B=\frac{1}{sin^{2}B } => 1+\frac{1}{tan^{2} B}=\frac{1}{sin^{2}B } \\=> 1+\frac{1}{\frac{5^{2} }{12^{2} } } =\frac{1}{sin^{2}B }\\ => sin^{2}B=\frac{25}{169}[/tex]
because B is in quadrant III => [tex]sin B=-\sqrt{\frac{25}{169} }=\frac{-5}{13}=>cosB=-\sqrt{1-\frac{5^{2} }{13^{2} } }=\frac{-12}{13}[/tex]
tan(arcsin(-4/5)+arctan(5/12)) = tan( A + B)
but A,B are the 2 angles of a triangle => tan(A + B) = [tex]\frac{sin(A+B)}{cos(A+B)}[/tex]
have: sin(A+B) = sinA.cosB + cosA.sinB = [tex]\frac{-4}{5}.\frac{-12}{13} +\frac{3}{5}.\frac{-5}{13}=\frac{33}{65}[/tex]
cos(A + B) = cosA.cosB - sinA.sinB =[tex]\frac{3}{5}.\frac{-12}{13}-\frac{-4}{5}.\frac{-5}{13}=\frac{-56}{65}[/tex]
=> tan(A + B) = [tex]\frac{33}{65}:\frac{-56}{65}=\frac{-33}{56}[/tex]
Answer:
pie/6
Explaniation:
just took the test on k12
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(
−
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Step-by-step explanation:
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Step-by-step explanation:
A barrel filled with oil is a cylinder with a diameter of 22 inches and a height of 35.5 inches. There are 231 cubic inches in a liquid gallon, how many gallons of oil does the barrel hold
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Step-by-step explanation:
Given : For cylinder , diameter = 22 inches and height = 35.5 inches
radius = 11 inches [half of diameter]
Volume of cylinder [tex]=\pi r^2h[/tex], where r= radius and h = height.
Volume of cylinder [tex]=\dfrac{22}{7}\times(11)^2\times 35.5=13500.14\text{ cubic inches}[/tex]
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What does x equal
Answers
Answer:
x = 0
Step-by-step explanation:
Given
- 4 = 3 + 7(x - 1) ← distribute and simplify right side
- 4 = 3 + 7x - 7
- 4 = 7x - 4 ( add 4 to both sides )
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We have the Equation:
x + 3x = 144
4x = 144
x = 144/4
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Therefore, the number of CDs in Walter's collection is 36 CDs
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Step-by-step explanation:
cause i ik
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