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].
The sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that 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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