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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
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