Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

The terminal side of angle θ intersects the unit circle in the first quadrant at x=2/5. What are the exact values of sinθ and cosθ?

Sagot :

sqdancefan

Answer:

  • sin(θ) = (√21)/5
  • cos(θ) = 2/5

Step-by-step explanation:

You want the exact values of sine and cosine of the angle whose terminal point is at x=2/5 on the unit circle in the first quadrant.

Pythagorean identity

The coordinates of a point on the unit circle are (cos(θ), sin(θ)). You already know that the x-coordinate is 2/5, so ...

  cos(θ) = 2/5

The Pythagorean identity in trigonometric terms is ...

  sin²(θ) +cos²(θ) = 1

Then the sine of the angle is ...

  sin(θ) = √(1 -cos²(θ))

  sin(θ) = √(1 -(2/5)²) = √((25 -4)/25)

  sin(θ) = (√21)/5

The exact values of sine and cosine are ...

  • sin(θ) = (√21)/5
  • cos(θ) = 2/5
View image sqdancefan
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.