QuestionAugust 27, 2025

If cosTheta approx 0.3090 which of the following represents approximate values of sinTheta and tanTheta , for 0^circ lt Theta lt 90^circ sinTheta approx 0.9511;tanTheta approx 0.3249 sinTheta approx 0.9511;tanTheta approx 3.0780 sinTheta approx 3.2362;tanTheta approx 0.0955 sinTheta approx 3.2362;tanTheta approx 10.4731

If cosTheta approx 0.3090 which of the following represents approximate values of sinTheta and tanTheta , for 0^circ lt Theta lt 90^circ sinTheta approx 0.9511;tanTheta approx 0.3249 sinTheta approx 0.9511;tanTheta approx 3.0780 sinTheta approx 3.2362;tanTheta approx 0.0955 sinTheta approx 3.2362;tanTheta approx 10.4731
If cosTheta approx 0.3090 which of the following represents approximate values of sinTheta  and tanTheta  , for 0^circ lt Theta lt 90^circ 
sinTheta approx 0.9511;tanTheta approx 0.3249
sinTheta approx 0.9511;tanTheta approx 3.0780
sinTheta approx 3.2362;tanTheta approx 0.0955
sinTheta approx 3.2362;tanTheta approx 10.4731

Solution
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Answer

sin\Theta \approx 0.9511; tan\Theta \approx 3.0780 Explanation 1. Calculate sin\Theta Use the identity sin^2\Theta + cos^2\Theta = 1. Thus, sin\Theta = \sqrt{1 - cos^2\Theta} = \sqrt{1 - (0.3090)^2} \approx \sqrt{1 - 0.0955} \approx \sqrt{0.9045} \approx 0.9511. 2. Calculate tan\Theta Use the identity tan\Theta = \frac{sin\Theta}{cos\Theta}. Thus, tan\Theta = \frac{0.9511}{0.3090} \approx 3.0780.

Explanation

1. Calculate $sin\Theta$<br /> Use the identity $sin^2\Theta + cos^2\Theta = 1$. Thus, $sin\Theta = \sqrt{1 - cos^2\Theta} = \sqrt{1 - (0.3090)^2} \approx \sqrt{1 - 0.0955} \approx \sqrt{0.9045} \approx 0.9511$.<br /><br />2. Calculate $tan\Theta$<br /> Use the identity $tan\Theta = \frac{sin\Theta}{cos\Theta}$. Thus, $tan\Theta = \frac{0.9511}{0.3090} \approx 3.0780$.
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