Quadrantal angles are angles that, when in standard position, have their terminal side lying on one of the coordinate axes (0°, 90°, 180°, 270°, 360° and so on). Evaluating trigonometric functions at these angles involves understanding that certain coordinates are 0 or ±1. This leads to some trig functions being undefined at certain quadrantal angles because of division by zero. Understanding these values is crucial for simplifying expressions and solving trigonometric equations.
When working with quadrantal angles, remember that on the unit circle, the coordinates of the points where the axes intersect the circle are (1, 0), (0, 1), (-1, 0), and (0, -1). These coordinates directly correspond to the cosine and sine values of the angles 0°, 90°, 180°, and 270° respectively. Use these values to find the other trigonometric functions.
Match the following terms with their definitions:
| Term | Definition |
|---|---|
| 1. Quadrantal Angle | A. The ratio of the opposite side to the hypotenuse in a right triangle. |
| 2. Sine (sin) | B. An angle whose terminal side lies on one of the coordinate axes. |
| 3. Cosine (cos) | C. Undefined for angles where the x-coordinate is zero. |
| 4. Tangent (tan) | D. The ratio of the adjacent side to the hypotenuse in a right triangle. |
| 5. Cosecant (csc) | E. Undefined for angles where the y-coordinate is zero. |
Complete the following paragraph by filling in the missing words.
At 0°, the coordinates on the unit circle are (1, 0). Therefore, the cosine is _____, and the sine is _____. The tangent at 90° is ________ because it involves division by zero.
Explain why the sine of 90° is 1, while the cosine of 90° is 0. Use the unit circle to support your explanation.
Please log in to post your answer.
Log InEarn 2 Points for answering. If your answer is selected as the best, you'll get +20 Points! 🚀