Calculating tan(7π/6) and sec(-π/4)

Trigonometry · Axiom Academy

EXAMPLE Evaluating Tangent and Secant Functions Learn to calculate tan and sec using sine and cosine values, and identify when functions are undefined. Excellent work! You've successfully evaluated both trigonometric functions. Here's what we learned: Tangent is the ratio of sine to cosine: tan(θ) = sin(θ)/cos(θ). Always check that cos(θ) ≠ 0 to avoid undefined values. Secant is the reciprocal of cosine: sec(θ) = 1/cos(θ). Secant is undefined whenever cosine equals zero. Use reference angles: For angles like 7π/6, identify the quadrant and reference angle (π/6) to determine sign and values. Rationalize when needed: Expressions like 1/√2 should be rationalized to √2/2 for standard form. Check for undefined values: Before calculating, verify the denominator isn't zero. For tan(θ), check cos(θ) ≠ 0. For sec(θ), check cos(θ) ≠ 0. These fundamental relationships between trig functions will help you evaluate any trigonometric expression. Always remember the reciprocal and quotient identities!

This is the written version of the interactive lesson above. See the full Trigonometry course.