- Difficulty
- Introductory
- Suggested time
- 3 min
- Marks
- 2
Functions, graphs and inverses practice question 5
Find the exact value of the expression below.
Evaluate each factor on the unit circle. For which factor is the angle outside the first quadrant, and what does that do to its sign?
Work out each factor on its own. , and lies in the second quadrant with reference angle .
An exact expression, or a decimal to three places.
Theory UBC Math 100 §1.5CLP-1 §0.4Key results
Worked solution
Strategy
Evaluate each factor on the unit circle, then multiply. For an angle outside the first quadrant, find the reference angle and the sign separately.
Working
5π/6 = π − π/6: second quadrant, reference angle π/6, cosine negative.
Tangent is sine over cosine.
Secant is the reciprocal of cosine.
Multiply.
Answer
The answer is negative 2 over root 3, about −1.155.
Check
Tangent is negative in the second quadrant, where 5π/6 lies, and |tan(5π/6)| < 1 while sec(π/3) = 2, so the product lies between −2 and 0.
Where this goes wrong
Losing the sign of tan(5π/6). In the second quadrant cosine is negative and sine is positive, so the tangent is negative.
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