Solving Cosine Equations

The video tutorial explains how to solve the trigonometric equation COS(x + 80°) = 0.7 within the range of 0 to 360 degrees. It begins by calculating the inverse cosine to find an initial solution, followed by sketching the cosine curve to identify two possible solutions. The tutorial then adjusts these solutions to fit within the specified range by adding the period of the cosine function. Finally, the video concludes with the two valid solutions to the problem.

What is the equation we are trying to solve in this tutorial?

• tan(x + 80°) = 0.7

• cos(x + 80°) = 0.7

• cos(x - 80°) = 0.7

• sin(x + 80°) = 0.7

What is the first step in solving the equation cos(x + 80°) = 0.7?

• Add 80 degrees to both sides

• Subtract 80 degrees from both sides

• Use inverse cosine on both sides

• Multiply both sides by 2

What is the initial solution for x + 80° after applying inverse cosine?

• 45.6 degrees

• 90 degrees

• 180 degrees

• 270 degrees

Why do we sketch the cosine curve in this problem?

• To determine the period of the function

• To check for symmetry

• To identify additional solutions

• To find the maximum value

How do we find the second solution for x + 80°?

• Divide 45.6 degrees by 2

• Multiply 45.6 degrees by 2

• Subtract 45.6 degrees from 360 degrees

• Add 45.6 degrees to 360 degrees

What are the two equations we work with after finding the solutions for x + 80°?

• x + 80 = 0 and x + 80 = 180

• x + 80 = 180 and x + 80 = 360

• x + 80 = 90 and x + 80 = 270

• x + 80 = 45.6 and x + 80 = 314.4

What is the solution for x after subtracting 80 degrees from 314.4 degrees?

• 234.4 degrees

• 45.6 degrees

• 90 degrees

• 180 degrees

What adjustment is made to the solution x = -34.4 to fit within the 0 to 360-degree range?

• Divide by 2

• Multiply by 2

• Add 360 degrees

• Subtract 360 degrees

What is the final solution for x after adjusting -34.4 degrees?

• 325.6 degrees

• 45.6 degrees

• 234.4 degrees

• 180 degrees

What is the period of the cosine function used in this problem?

• 180 degrees

• 360 degrees

• 90 degrees

• 270 degrees