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Find all solutions to 2 cos t = 0.35 for 0 ≤ t ≤ 2π Give...


Find all solutions to 2 cos t = 0.35 for 0 ≤ t ≤ 2π Give answers correct to 3 decimal places. Give answers in degrees.

Math   Precalculus   
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Homework Answers

Answer #1

At first remind a general form of cosine function which is

In 0<=A<=2π, cosA=cos(4×π/2 -A). -------(1) taking this into account we proceed to solve the given equation.

Given that 2cost = 0.35

Or, cost = 0.35/2 = 0.175

Or, t = cos^-1 (0.175) = 79.921°

Thus we can write cost = cos(79.921°)

Again cos(79.921°)= cos(4×90°-79.921) ( from the discussion above (1) )

So t= 79.921° and (4×90°-79.921°)

That is t = 79.921° , 280.079 are the solutions in

0<=t<=2π

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