Given cot A=5/2 and that angle A is in quadrant I, find the exact value of sin A in simplest radical form using a rational denominator
Answers
Answer:Given cot A = 3 over 7 and that angle A is in Quadrant I, find the exact value of cos A in simplest radical form using a rational denominator ... √58=c. cos = 3/√58 To rationalize, multiply the numerator and denominator by √58 ... how do i go about solving a trig identity; that simplify s 1-sin^2 theta/1-cos theta.
Step-by-step explanation:
The value of sin A is [tex]\frac{2\sqrt{29} }{29}[/tex].
What is sine of an angle?
The sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle.
What is tangent of an angle?The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
According to the given question.
We have [tex]cotA = \frac{5}{2}[/tex]
⇒[tex]tanA = \frac{2}{5}[/tex]
From the definition of tangent of an angle.
In right angled triangle PQR, we can say that
PR = 2 and RQ = 5
Therefore,
[tex]x^{2} = (PR)^{2} +(RQ)^{2}[/tex]
⇒[tex]x^{2} =(2)^{2} +(5)^{2}[/tex]
⇒[tex]x^{2} = 4 + 25[/tex]
⇒[tex]x^{2} = 29[/tex]
⇒[tex]x = \sqrt{29}[/tex]
Since,
Sine of an angle = opposite side/ Hypotenuse
In triangle PQR
The opposite side w.r.t angle A is PR.
And the hypotenuse is PQ.
Therefore, sine of an angle A is given by
[tex]sinA= \frac{2}{\sqrt{29} }[/tex]
⇒[tex]sinA = \frac{2}{\sqrt{29} } \frac{\sqrt{29} }{\sqrt{29} }[/tex]
⇒[tex]sinA = \frac{2\sqrt{29} }{29}[/tex]
Hence, the value of sin A is [tex]\frac{2\sqrt{29} }{29}[/tex].
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Subtract and then simplify
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Chad bought 8 dozen note pads for his office. The note pads were divided equally into 6 boxes. How many note pads are in each box? (Hint: a dozen is equal to 12) *
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9514 1404 393
Answer:
5) (x, y) = (10, -1)
6) (x, y) = (5, 6)
Step-by-step explanation:
5) y coefficients are opposites, so y can be eliminated by adding the two equations.
(x -y) +(2x +y) = (11) +(19)
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Using the second equation, we can find y:
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__
6) The x-coefficients are the same, so we can eliminate the x-term by subtracting the second equation from the first. We choose to do it that way so the y-coefficient ends up positive.
(-6x +6y) -(-6x +3y) = (6) -(-12)
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In a right triangle, the leg adjacent to an angle of 23° is 12 cm long. How long is the leg opposite the 23° angle, to the nearest tenth?
Answers
Answer:
tan55 = x/43
x = tan(55) * 43
x = 61.4 cm
Step-by-step explanation:
The length of the leg opposite the 23° angle, to the nearest tenth, will be 5.1 cm.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
In a right triangle, the leg adjacent to an angle of 23° is 12 cm long. The triangle is given below.
Let 'x' be the opposite side of the angle 23°. Then the value of the variable 'x' is given as,
tan 23° = x / 12
Simplify the equation, then we have
tan 23° = x / 12
0.4244 = x / 12
x = 0.4244 · 12
x = 5.1 cm
The length of the leg opposite the 23° angle, to the nearest tenth, will be 5.1 cm.
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
9514 1404 393
Answer:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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