Solving Trig Equations — Question 10

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Question 10

Solve the equation sec⁡(x)=2\sec(x) = 2 for all x∈[0,2π]x \in [0, 2\pi].

Original worksheet page 1: question and worked solution for 1-4-010
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Question 10 - Solution

Step 1: Recall the definition of secant: sec⁡(x)=1cos⁡(x)⇒1cos⁡(x)=2⇒cos⁡(x)=12\sec(x) = \frac{1}{\cos(x)} \Rightarrow \frac{1}{\cos(x)} = 2 \Rightarrow \cos(x) = \frac{1}{2}

Step 2: Solve cos⁡(x)=12\cos(x) = \frac{1}{2} in [0,2π][0, 2\pi]:

The cosine is 12\frac{1}{2} at: x=π3,5π3x = \frac{\pi}{3},\ \frac{5\pi}{3}

x=π3,5π3\boxed{x = \frac{\pi}{3},\ \frac{5\pi}{3}}

Original worksheet page 2: question and worked solution for 1-4-010

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