if cos theta = -3/5 in quadrant 2, what is sin theta?

Question

contestada

Respuesta :

dhiab dhiab · Answer 1 · 2019-04-26T21:09:48+02:00

Answer:

hello : sin(θ) = 4/25

Step-by-step explanation:

you know : cos²(θ) + sin²(θ) =1 and : cos(θ) = - 3/5

(-3/5)² + sin²(θ) =1

9/25 + sin²(θ) =1

sin²(θ) =1 -9/25

sin²(θ) = 16/25

sin(θ) = 4/25 or sin(θ) = - 4/25

in quadrant 2 : sin(θ) > 0

so : sin(θ) = 4/25

Answer Link

lisboa lisboa · Answer 2 · 2019-06-19T21:26:55+02:00

Answer:

[tex]sin(theta)=\frac{4}{5}[/tex]

Step-by-step explanation:

if cos theta = -3/5 in quadrant 2, find out sin(theta)

[tex]cos(x)=\frac{-3}{5}[/tex]

cos is negative in second and third quadrant

Here cos is in second quadrant.

Sin is positive in second quadrant .

[tex]cos(x)=\frac{adjacent}{hypotenuse}[/tex]

adjacent side= 3 , hypotenuse = 5

Lets use Pythagorean theorem [tex]c^2=a^2 + b^2[/tex]

[tex]5^2=3^2 + b^2[/tex]

[tex]25=9 + b^2[/tex] Subtract 9 from both sides

[tex]b^2= 16[/tex]

b=4

opposite side = 4

[tex]sin(x)=\frac{opposite}{hypotenuse}[/tex]

[tex]sin(theta)=\frac{4}{5}[/tex]