How Does Quadrant Affect Values in Trigonometric Functions?

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SUMMARY

The discussion centers on determining the cosine value for an angle where the tangent is given as -√3 and the angle lies in the third quadrant. The participants clarify that if tan(b) = -√3, then the angle b should be correctly identified as being in quadrant II or IV, not III. The sine value is calculated as sin(b) = -√3 / 2, leading to the conclusion that the cosine value, cos(b), is -1/2 based on the relationship cos = x/r, where x and r are derived from the coordinates in the unit circle.

PREREQUISITES
  • Understanding of trigonometric functions and their relationships
  • Knowledge of the unit circle and quadrants
  • Familiarity with the Pythagorean theorem in trigonometry
  • Ability to manipulate square roots and rational expressions
NEXT STEPS
  • Study the properties of trigonometric functions in different quadrants
  • Learn how to derive sine and cosine values from tangent
  • Explore the unit circle and its application in trigonometry
  • Investigate the Pythagorean identities and their proofs
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Students of trigonometry, mathematics educators, and anyone looking to deepen their understanding of trigonometric functions and their applications in various quadrants.

CrossFit415
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How would I find cos for tan when..

Tan b = (-√3)

Theta lies in quadrant iii

Sin b would equal (-√3) / 2

So Cos b would equal -1 / 2?
 
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y: -√3
x: 1
r: √2 > from x2 + y2

cos = x/r

Answer: ?
 
CrossFit415 said:
How would I find cos for tan when..

Tan b = (-√3)

Theta lies in quadrant iii
What does theta have to do with anything? Assuming that you meant b instead of theta, if tan(b) = -√3, then b is in quadrant II or quadrant IV.
CrossFit415 said:
Sin b would equal (-√3) / 2

So Cos b would equal -1 / 2?
 

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