Solving Trigonometric Equations

This video tutorial covers solving trigonometric equations, focusing on cosine, sine, and tangent functions. It explains how to find solutions using symmetry and graph analysis, including handling negative values. The tutorial also introduces advanced equations requiring rearrangement and new notation. Viewers are encouraged to practice with linked exam questions.

What is the first step in solving the equation cos(x) = 0.8?

• Subtract 0.8 from both sides

• Add 1 to both sides

• Take the inverse cosine of both sides

• Multiply both sides by 2

How do you find the second solution for cos(x) = 0.8 using the graph?

• Subtract the first solution from 360 degrees

• Add 90 degrees to the first solution

• Multiply the first solution by 2

• Divide the first solution by 2

What is the first solution for cos(x) = -0.2?

• 101.5 degrees

• 323.1 degrees

• 258.5 degrees

• 36.9 degrees

What is the exact value of cos(60 degrees)?

• 0.8

• 1

• 0.2

• 0.5

What is the first solution for sine(x) = 0.3?

• 17.5 degrees

• 162.5 degrees

• 135 degrees

• 45 degrees

What is the exact value of sine(45 degrees)?

• 1

• 0.3

• sqrt(2)/2

• 0.5

How do you find solutions for sine(x) = -0.4?

• Multiply by 2

• Use symmetry and subtract 180 degrees

• Divide by 2

• Use symmetry and add 360 degrees

What is the first solution for tan(x) = 3.5?

• 74.1 degrees

• 254.1 degrees

• 309.8 degrees

• 129.8 degrees

How do you find the second solution for tan(x) = -1.2?

• Divide the first solution by 2

• Multiply the first solution by 2

• Subtract 180 degrees from the first solution

• Add 180 degrees to the first solution

What is the first step in solving 4sin(x) = 3?

• Add 3 to both sides

• Multiply both sides by 4

• Divide both sides by 4

• Subtract 3 from both sides