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Byte of Accounting, Inc.General JournalNeed help with 27 through.pdf

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Calculate sin 2x if tan x=3 and x is in (0 , 90)? Solution Since x is in the first quadrant, then the values of the trigonometric functions are positive. We\'ll write the formula for sin 2x: sin 2x = sin (x+x) sin (x+x) = sinx*cosx + sinx*cosx sin (x+x) = 2 sinx*cos x We know that the tangent function is a ratio of sine and cosine functions: tan x = sin x/cos x tan x = 3 => sin x/cos x = 3 => sin x = 3 cos x sin 2x = 2*3cos x*cosx = 6 (cos x)^2 We know that: 1 + (tan x)^2 = 1/(cos x)^2 1 + 9 = 1/(cos x)^2 10 = 1/(cos x)^2 (cos x)^2 = 1/10 sin 2x = 6/10 sin 2x = 3/5.

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Byte of Accounting, Inc.General JournalNeed help with 27 through.pdfajantha11

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- Calculate sin 2x if tan x=3 and x is in (0 , 90)? Solution Since x is in the first quadrant, then the values of the trigonometric functions are positive. We'll write the formula for sin 2x: sin 2x = sin (x+x) sin (x+x) = sinx*cosx + sinx*cosx sin (x+x) = 2 sinx*cos x We know that the tangent function is a ratio of sine and cosine functions: tan x = sin x/cos x tan x = 3 => sin x/cos x = 3 => sin x = 3 cos x sin 2x = 2*3cos x*cosx = 6 (cos x)^2 We know that: 1 + (tan x)^2 = 1/(cos x)^2 1 + 9 = 1/(cos x)^2 10 = 1/(cos x)^2 (cos x)^2 = 1/10 sin 2x = 6/10 sin 2x = 3/5

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