How do you solve $y = 2 cos 3 (x - (\frac{π}{4}))$ $y = 2 cos 3 (x - (pi/4))$ ?

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Answer 1 · 2015-04-27T16:34:05

Solve $y = 2. cos 3(x - Pi/4) = 0$ .

Call $(x - Pi/4) = t -> y = 2. cos 3t = 0$

$cos 3t = 0 --> 3t = Pi/2; and 3t = 3Pi/2$

$3t = Pi/2 -> t = Pi/6 (1)$

$3t = 3Pi/2 -> t = Pi/2 (2)$

$(1) t = (x - Pi/4) = Pi/6 -> x = 5Pi/12$

$(2) t = (x - Pi/4) = Pi/2 -> x = Pi/2 + pi/4 = 6Pi/8 = 3Pi/4$

Answer:

$x = 5Pi/12 and x = 3Pi/4$

Check:

(1) $x = 5Pi/12 -> t = x - Pi/4 = 5Pi/12 - Pi/4 = Pi/6 -> 3t = 3Pi/6 = Pi/2 -> cos 3t = cos Pi/2 = 0$ .

Correct.

(2) $x = 3Pi/4 -> t = (x - Pi/4) = 3Pi/4 - Pi/4 = Pi/2 -> 3t = 3Pi/2 -> cos 3t = cos 3Pi/2 = 0$ .

Correct.

How do you solve y = 2 cos 3 (x - (pi/4))y=2cos3(x−(π4))y = 2 cos 3 (x - (pi/4))?