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Consider this equation.


sin(θ)= 3sqrt10/10


If θ is an angle in quadrant II, what is the value of tan(θ) ?

Consider This Equationsinθ 3sqrt1010If Θ Is An Angle In Quadrant II What Is The Value Of Tanθ class=

Sagot :

altavistard

Answer:

tan x = -3 (Answer A)

Step-by-step explanation:

We want to find the tangent of this angle "theta," and recall the trig identity

(sin x)^2 + (cos x)^2 = 1.

               3√10

If sin x = -----------

                   10

                             90

then (sin x)^2 = ----------- = 9/10

                             100

and (cos x)^2 = 1 - 9/10 = 1/10

 

                      sin x       3√10/10

Then tan x = ---------- = -------------- = -3 (Answer A)

                       cos x      1√10/10

The tangent function is negative in Quadrant II.  In Quadrant I tan x = +3

Answer:

A

Step-by-step explanation:

Using the trig identity

sin²x + cos²x = 1 , then cos x = ± [tex]\sqrt{1-(\frac{3\sqrt{10} }{10})^2 }[/tex]

Given

sinθ = [tex]\frac{3\sqrt{10} }{10}[/tex] , then

cosθ = ± [tex]\sqrt{1-(\frac{3\sqrt{10} }{10})^2 }[/tex]

        = ± [tex]\sqrt{1-\frac{9}{10} }[/tex]

        = ± [tex]\sqrt{\frac{1}{10} }[/tex]

Since θ is in second quadrant where cosθ < 0 , then

cosθ = - [tex]\frac{1}{\sqrt{10} }[/tex]

Then

tanθ = [tex]\frac{sin0}{cos0}[/tex] = [tex]\frac{\frac{3\sqrt{10} }{10} }{\frac{-1}{\sqrt{10} } }[/tex] = - 3 → A

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