Notes on quadrants

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Notes on quadrants

  1. 1. Topic 2-4 Trig Functions
  2. 2. Learning Goal To determine the values of the six trigonometric ratios in a right triangle.
  3. 3. Defining Trig Functions r θ Let there be a point P (x, y) on a coordinate plane. r is the distance from the origin to the point P, which can be represented as being on the terminal side of θ. Since r represents a distance, it is always positive. P(x, y)
  4. 4. Trig Functions For a given value of θ, the ratios of y/r, x/r and y/x are constant because of similar triangles, thereby satisfying the requirement of a function that for each x-value (or, in this case, θ) there is only one y-value.
  5. 5. Finding Trig Function Values - 1 If the terminal side of θ in standard position passes through point P (6, 8), draw θ and find the exact value of the six trig functions of θ. P(6, 8) θ 8 6 r = 10
  6. 6. Finding Trig Function Values - 2 If the terminal side of θ in standard position passes through point P (-4, 2), draw θ and find the exact value of the six trig functions of θ. P(-4, 2) θ 2 -4 r = 2√5
  7. 7. Positive Trig Function Values r r r r x -x y y -y -y All trig functions are positive. Sine is positive. (So is cosecant.) Tangent is positive. (So is cotangent.) Cosine is positive. (So is secant.)
  8. 8. Determining The Quadrant - 3 In which quadrant is θ if cos θ and tan θ have the same sign? Quadrants I and II
  9. 9. Determining The Quadrant - 4 In which quadrant is θ if cos θ is negative and sin θ is positive? Quadrant II
  10. 10. Determining The Quadrant - 5 In which quadrant is θ if cot θ and sec θ have opposite signs? Quadrants III and IV
  11. 11. Find values - 1 Find the exact values of the other five trig functions for an angle θ in standard position, given 3π/2 2π 13 -5 12 θ
  12. 12. Find values - 2 Find the exact values of the other five trig functions for an angle θ in standard position, given π 2π 2 -1 θ -√3

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