SUMMARY
The discussion focuses on determining the value of cscØ given cosØ = 1/2 and a negative tanØ. It establishes that cscØ is the reciprocal of sinØ, and since cosØ is positive, sinØ must be negative. Using the Pythagorean identity sin²Ø + cos²Ø = 1, the value of sinØ is derived as -√(3/4), leading to cscØ = -2/√3 or -2√3/3. The final conclusion is that the correct answer is option d) -2√3/3.
PREREQUISITES
- Understanding of trigonometric identities, specifically sin²Ø + cos²Ø = 1.
- Knowledge of the relationships between sine, cosine, and tangent functions.
- Familiarity with the concept of cosecant as the reciprocal of sine.
- Ability to manipulate square roots and fractions in mathematical expressions.
NEXT STEPS
- Study the Pythagorean identity in trigonometry and its applications.
- Learn how to derive trigonometric values from given angles using identities.
- Practice solving problems involving the reciprocal trigonometric functions.
- Explore the unit circle and its significance in determining the signs of trigonometric functions in different quadrants.
USEFUL FOR
Students preparing for trigonometry exams, educators teaching trigonometric identities, and anyone seeking to deepen their understanding of sine, cosine, and cosecant relationships.