Grade 9 Math: Cotangent Worksheet
This worksheet focuses on understanding and calculating the cotangent function in trigonometry for Grade 9 students.
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Grade 9 Math: Cotangent
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Read each question carefully and provide the best answer. Show all your work where applicable.
1. The cotangent function is the reciprocal of the function.
2. For an angle $\theta$ in a right-angled triangle, cot($\theta$) = $\frac{\text{ }}{\text{opposite}}$.
3. The cotangent of an angle is undefined when the component of the point on the unit circle is zero.
4. If tan($\theta$) = $\frac{3}{4}$, what is cot($\theta$)?
$\frac{3}{4}$
$\frac{4}{3}$
$1$
Undefined
5. Which of the following angles has an undefined cotangent value?
$30^\circ$
$90^\circ$
$180^\circ$
$270^\circ$
6. Given a right triangle with an adjacent side of 5 units and an opposite side of 12 units, find the cotangent of the angle.
7. Explain why cot($0^\circ$) is undefined using the unit circle definition of cotangent.
8. The range of the cotangent function is all real numbers.
True
False
9. Cotangent is positive in the second and fourth quadrants.
True
False
10. Sketch one period of the graph of y = cot(x) on the coordinate plane below. Label the asymptotes and key points.