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
USEFUL FOR
Students of trigonometry, mathematics educators, and anyone looking to deepen their understanding of trigonometric functions and their applications in various quadrants.