Lassakhadijah57idn
Answered

Join the IDNLearn.com community and get your questions answered by experts. Our Q&A platform is designed to provide quick and accurate answers to any questions you may have.

Given that 4cos∅ + 3sin∅ = 5, find the value of: (a) sin∅ (b) tan∅ © cot∅.​

Sagot :

Mhanifaidn

Answer:

Given:

  • 4 cosθ + 3 sinθ = 5

Use identity:

  • sin²θ + cos²θ = 1

Apply to the given expression, substitute cosθ:

  • 4√(1 - sin²θ) + 3 sinθ = 5
  • 4√(1 - sin²θ) = 5 - 3 sinθ

Square both sides:

  • 16(1 - sin²θ) = 25 - 30sinθ + 9sin²θ
  • 16 - 16sin²θ = 25 - 30sinθ + 9sin²θ
  • 25sin²θ - 30sinθ + 9 = 0
  • (5sinθ - 3)² = 0
  • 5sinθ - 3 = 0
  • sinθ = 3/5

Find cosθ:

  • cosθ = √(1 - 9/25) = √16/25 = 4/5

Find tanθ:

  • tanθ = sinθ / cosθ = (3/5)/(4/5) = 3/4

Find cotθ:

  • cotθ = 1/tanθ = 1/(3/4) = 4/3
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.