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Natalie Goodwin

Feb 20, 2025

If sin x = .21,what is cos x?

I need help with my homework!!!here are the answer choices a: .76 b: .98 c: .87 d: .65
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6 Answers

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Miss Alice Doyle

Feb 20, 2025

Start with the following trigonometric identity: sin^2(x) + cos^2(x) = 1sin^2(x) + cos^2(x) = 1cos^2(x) = 1 – sin^2(x)cos(x) = (+/-)sqrt(1 – sin^2(x))cos(x) = (+/-)sqrt(1 – .21^2) = +/-0.98, which matches choice b. However, this is only the case if x is in Quadrant I, i.e., 0 to pi/2 radians or 0 to 90 degrees. You could have sin(x) = .21 with x in Quadrant II, i.e., pi/2 to pi radiants or 90 to 180 degrees, and then cos(x) would be -.98, not .98.... Show More
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Miss Alice Doyle

Feb 20, 2025

Sin x = 0.21 = 21/100 = o/h To find the adjacent ‘a’ use Pythagoras. 21^2 + a^2 = 100^2 a^2 = 100^2 – 21^2a^2 = (100 – 21)(100 + 21)a^2 = 79 x 121a^2 = 9559a = sqrt (9559) = 97.77…Cos x = a/h = 97.77.. / 100Cos x = 0.977777…Cos x = 0.98 ==> ‘b’... Show More
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Miss Alice Doyle

Feb 20, 2025

Since sin x = .21, the opposite side equals .21 and the hypotenuse is 1.By the Pythagorean Theorem, the adjacent side is √(1^2 – .21^2) = 0.978So, cos x = 0.978 / 1 = 0.978... Show More
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Miss Alice Doyle

Feb 20, 2025

(sin x)^2 + (cos x)^2 = 1therefore cos x = sqrt (1-.21^2) = 0.98... Show More
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Miss Alice Doyle

Feb 20, 2025

Sine squared plus cosine squared = 1, so:0.21^2 = 0.04411 – 0.0441 = 0.95590.9559^(1/2) = 0.9777... Show More
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Miss Alice Doyle

Feb 20, 2025

sin(x) = 0.21cos(x) = √(1 – sin²(x)) = √(1 – (0.21)²) = .98... Show More
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