Determine the values

[xerxe1s]

Determine the values of sin 2θ , cos 2θ and tan 2θ , given cosθ = − 4/5 and π/2 ≤θ ≤ π
we just learned this in class and im confused how to solve it

 

[Deleted member 4993]

Determine the values of sin 2θ , cos 2θ and tan 2θ , given cosθ = − 4/5 and π/2 ≤θ ≤ π
we just learned this in class and im confused how to solve it

Can you express sin(Θ) as a function of cos(Θ)

 

[xerxe1s]

Can you express sin(Θ) as a function of cos(Θ)

yes or at least i have been doing it

 

[Deleted member 4993]

yes or at least i have been doing it

What is that function?

Please share your work.

 

[xerxe1s]

i havent done this question because I have no idea how to do it my class examples dont help

 

[Deleted member 4993]

i havent done this question because I have no idea how to do it my class examples dont help

Do you recall the following relation:

cos²(Θ) + sin²(Θ) = 1

 

[JeffM]

In addition to the identity mentioned by Subhotosh Khan, you should have been taught formulas for:

[MATH]sin( \theta + \phi)[/MATH] and [MATH]cos( \theta + \phi)[/MATH].

From those basic formulas, it is easy to derive formulas for

[MATH]sin(2 \theta) = sin( \theta + \theta) [/MATH] and [MATH]cos (2 \theta ) = cos( \theta + \theta).[/MATH]
Do you your notes or text reference any of these formulas?

 

[Steven G]

Determine the values of sin 2θ , cos 2θ and tan 2θ , given cosθ = − 4/5 and π/2 ≤θ ≤ π
we just learned this in class and im confused how to solve it

π/2 ≤θ ≤ π implies that π ≤ 2θ ≤ 2π (I just doubled all 3 sides) So 2θ is in quadrant 3 and 4.

Draw the triangle that obeys cosθ = 4/5 in quadrant 1. Label all 3 sides. Now sin2θ = 2sinθcosθ.The sin function is negative in quadrant 3 and 4 where 2θ lies. So we know that sin2θ will be negative. Now compute 2*sinθ*cosθ and whatever that equals sin2θ will be negative that value.

Try to do what I said and post back showing your work including a diagram.