Solve $\cos(x) = 0.69$ on $0 \leq x < 2\pi$ .
There are two solutions, $A$ and $B$ , with $A < B$ .
Give your answers accurate to 3 decimal places.

Question :

Solve $\cos(x) = 0.69$ on $0 \leq x < 2\pi$ .
there are two solutions, $a$ and $b$ , with $a < b$ .
give your answers accurate to 3 decimal places.

$Solve \cos(x) = 0.69 on 0 \leq x < 2\pi.there are two solutions, $ a | Doubtlet.com$

Solution:

Neetesh Kumar | October 15, 2024

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Assignment 9.5 Question 4: - on Solving Trignometric Equations
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Step-by-step solution:

We are given the equation:

$\cos(x) = 0.69$

Step 1: Find the reference angle

To find the reference angle, we take the inverse cosine:

$x = \cos^{-1}(0.69) \approx 0.809$

This is the reference angle in the first quadrant.

Step 2: Determine the solutions

Since cosine is positive in the first and fourth quadrants, we have two solutions:

In the first quadrant:
$A = 0.809$
In the fourth quadrant:
$B = 2\pi - 0.809 \approx 5.474$

Step 3: Write the solutions

Thus, the solutions are:

$A = \boxed{0.809}$ (rounded to 3 decimal places)

$B = \boxed{5.474}$ (rounded to 3 decimal places)

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Solve cos⁡(x)=0.69\cos(x) = 0.69cos(x)=0.69 on 0≤x<2π0 \leq x < 2\pi0≤x<2π. There are two solutions, AAA and BBB, with A<BA < BA<B. Give your answers accurate to 3 decimal places.