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An angle theta is between 270° and 360° and sin² theta = 0.36. Find all the trigonometric ratios without using a calculator.​

User Shadi
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Answer:

sin2θ=−0.96Explanation:270o<θ<360o tells us that we're working in the third quadrant, where sine is negative, while cosine is positive. Keep this in mind.Now, recall the identitysin2θ+cos2θ=1We know cosθ=0.6,cos2θ=(0.6)2=0.36So,0.36+sin2θ=1sin2θ=1−0.36sin2θ=0.64sinθ=±√0.64=±0.8As mentioned earlier, sine in quadrant III is negative, so we want the negative answer.sinθ=−0.8Now, we want sin2θ. Recall the identity sin2θ=2sinθcosθ. We have both sine and cosine, so we can plug them in:sin2θ=2(0.6)(−0.8)sin2θ=−0.96

Explanation:

User Matths
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