Question

Consider this equation.

Answer 1

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 2

Answer:

A

Step-by-step explanation:

Using the trig identity

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

Given

sinθ = $\frac{3\sqrt{10} }{10}$ , then

cosθ = ± $\sqrt{1-(\frac{3\sqrt{10} }{10})^2 }$

        = ± $\sqrt{1-\frac{9}{10} }$

        = ± $\sqrt{\frac{1}{10} }$

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

cosθ = - $\frac{1}{\sqrt{10} }$

Then

tanθ = $\frac{sin0}{cos0}$ = $\frac{\frac{3\sqrt{10} }{10} }{\frac{-1}{\sqrt{10} } }$ = - 3 → A