Quadrant Sign Quadrant Sign sin 230° sin 123° cos 67° cos 190° tan 160° tan 280° sin 15° sin 350° cos 350° cos 175° tan 35° tan 265°

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Trigonometric Angles: Quadrants and Signs

The table below asks you to determine the quadrant in which each given angle lies and whether the trigonometric value (sine, cosine, or tangent) is positive or negative within that quadrant. 

#### Table:

| Angle    | Quadrant | Sign  |
|----------|----------|-------|
| sin 230° |          |       |
| cos 67°  |          |       |
| tan 160° |          |       |
| sin 15°  |          |       |
| cos 350° |          |       |
| tan 35°  |          |       |
| sin 123° |          |       |
| cos 190° |          |       |
| tan 280° |          |       |
| sin 350° |          |       |
| cos 175° |          |       |
| tan 265° |          |       |

Each trigonometric function (sine, cosine, tangent) can have either a positive or negative value depending on the quadrant in which the angle is located:

- **Quadrant I**: 0° < angle < 90°
  - Sine: Positive
  - Cosine: Positive
  - Tangent: Positive

- **Quadrant II**: 90° < angle < 180°
  - Sine: Positive
  - Cosine: Negative
  - Tangent: Negative

- **Quadrant III**: 180° < angle < 270°
  - Sine: Negative
  - Cosine: Negative
  - Tangent: Positive

- **Quadrant IV**: 270° < angle < 360°
  - Sine: Negative
  - Cosine: Positive
  - Tangent: Negative

Using this information, you can determine both the quadrant and the sign for each angle given in the table.
Transcribed Image Text:### Trigonometric Angles: Quadrants and Signs The table below asks you to determine the quadrant in which each given angle lies and whether the trigonometric value (sine, cosine, or tangent) is positive or negative within that quadrant. #### Table: | Angle | Quadrant | Sign | |----------|----------|-------| | sin 230° | | | | cos 67° | | | | tan 160° | | | | sin 15° | | | | cos 350° | | | | tan 35° | | | | sin 123° | | | | cos 190° | | | | tan 280° | | | | sin 350° | | | | cos 175° | | | | tan 265° | | | Each trigonometric function (sine, cosine, tangent) can have either a positive or negative value depending on the quadrant in which the angle is located: - **Quadrant I**: 0° < angle < 90° - Sine: Positive - Cosine: Positive - Tangent: Positive - **Quadrant II**: 90° < angle < 180° - Sine: Positive - Cosine: Negative - Tangent: Negative - **Quadrant III**: 180° < angle < 270° - Sine: Negative - Cosine: Negative - Tangent: Positive - **Quadrant IV**: 270° < angle < 360° - Sine: Negative - Cosine: Positive - Tangent: Negative Using this information, you can determine both the quadrant and the sign for each angle given in the table.
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