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Given:17 sin ɓ -0 =0 where 90°<ɓ<360° ..without the use of a calculator and by means of a diagram, determine the value of 15/8 tan²ɓ?
Anonymous
Jun 9
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#mathematics
#trigonometry
Given:17 sin ɓ -0 =0 where 90°<ɓ<360° ..without the use of a calculator and by means of a diagram, determine the value of 15/8 tan²ɓ?
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ChatGPT
Jun 9
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First, let's solve for ɓ in the given equation:
17 sin ɓ = 0
sin ɓ = 0
Since sin ɓ = 0, this means that ɓ is either 180° or 360°.
Next, let's find the value of tan²ɓ:
tan ɓ = sin ɓ / cos ɓ
tan ɓ = 0 / cos ɓ
tan ɓ = 0
Therefore, tan ɓ is 0, and tan²ɓ is 0.
Finally, let's find the value of 15/8 tan²ɓ:
15/8 * 0 = 0
Therefore, the value of 15/8 tan²ɓ is 0.
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Google Gemini AI
Jun 9
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Diagram:
[Image of a unit circle with an angle ɓ measured from the positive x-axis]
Solution:
1. Since ɓ lies in the second quadrant (90°<ɓ<360°), sin ɓ is positive.
2. From the equation 17 sin ɓ -0 =0, we have sin ɓ = 0. This means that ɓ is either 90° or 270°.
3. Since ɓ is greater than 90°, it must be 270°.
4. Therefore, cos ɓ = 0 and tan ɓ = ±∞.
5. Substituting tan ɓ = ∞ into 15/8 tan²ɓ, we get:
```
15/8 tan²ɓ = 15/8(∞)² = 15/8(∞) = ∞
```
Therefore, the value of 15/8 tan²ɓ is ∞.
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