Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

HELP ASAP I WILL GIVE BRAINLIST

If sin ∅ = -sqrt{3} OVER 2 and π < ∅ < 3π OVER 2, what are the values of cos ∅ and tan ∅? What is ∅ in degrees and radians? Be sure to show and explain all work.

Sagot :

Step-by-step explanation:

sin ∅ = -(√3)/2

Note that

cos²∅ + sin²∅ = 1

cos²∅ = 1 - sin²∅

= 1 - (-√3 / 2)²

= 1 - (-√3)²/ 2²

= 1 - 3/4

= 1/4

cos²∅ = 1/4

Taking square root of both sides

cos∅ = 1/2

Note that tan∅ = sin∅/cos∅

therefore, tan∅ = -(√3)/2 ÷ 1/2

= -(√3)/2 × 2/1

= -√3

tan∅ = -√3

Since sin∅ = -√3 /2

Then ∅ = -60⁰

The value of ∅ for the given range (third quadrant) is 240⁰.

NB: sin∅ = sin(180-∅)

Also, since 180⁰ is π radians, then ∅ = 4π/3