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^{2}(x) - sin

^{2}(x) = [(√15/4)(√15/4)] - (1/4)(1/4) = 15/16 - 1/16 = 14/16 = 7/8

If sin(x) = 1/4 and x is in quadrantI,find the exact values of the expressions without solving for x.

(a) sin(2x)

(b) cos(2x)

(c) tan(2x)

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Hi again, Lauren.

A triangle is worth a zillion words...

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Remember that sin(x) = opposite side/hypotenuse. So on our triangle, we are going to put the angle x in the bottom left vertex. That makes the vertical leg the opposite leg = 1 and the hypotenuse = 4

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Now use the Pythag Thm to determine that the horizontal leg √15. So the cos(x)=(√15)/4

If you are not to solve for "x", can you use the trig double angle formulas?

a) sin(2x) = 2sin(x)cos(x) = 2(1/4)(√15)/4 = (1/2)(√15)/4 = (√15)/8

b) cos(2x) = cos^{2}(x) - sin^{2}(x) = [(√15/4)(√15/4)] - (1/4)(1/4) = 15/16 - 1/16 = 14/16 = 7/8

c) tan(2x) = [sin(2x)/cos(2x)] = [√15/8]/[7/8] = (√15)/7

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Use the Pythagorean Theorem to find the length of the adjacent side in the right triangle in Quad I.

a^{2} + 1^{2} = 4^{2}

a^{2} = 15, a = √15

cos x = (√15)/4 tan x = 1/√15 = √15/15

Now use these formulas:

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## Comments

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