Trigonometric Functions and Applications

Professor Dave explains how to solve trigonometric equations, starting with basic concepts like angles of elevation and moving to more complex equations. He demonstrates using tangent to find angles and solve equations, emphasizing the importance of understanding multiple solutions. The video covers solving equations with sine, cosine, and tangent, including quadratic forms and factoring. It concludes with strategies using trigonometric identities.

What is the primary trigonometric function used to find the angle of elevation?

• Tangent

• Cosine

• Secant

• Sine

If a building is 30 meters tall and casts a shadow of 16 meters, what is the angle of elevation of the sun?

• 62 degrees

• 75 degrees

• 60 degrees

• 45 degrees

How can you determine the height of a building using trigonometry if you know the distance and angle of elevation?

• Use the sine function

• Use the secant function

• Use the cosine function

• Use the tangent function

What is the height of a building if the distance is 100 meters and the angle of elevation is 55.3 degrees?

• 160 meters

• 144 meters

• 120 meters

• 100 meters

In the equation 4 sin X + 1 = 2 sin X + 2, what is the first step to solve for X?

• Divide both sides by 2

• Multiply both sides by 2

• Subtract 2 sin X from both sides

• Add 2 sin X to both sides

What is the sine value of pi/6?

• 1/2

• 0

• √3/2

• 1

Which of the following is a solution for sin X = 1/2?

• pi/2

• pi/4

• pi/6

• pi/3

What is the general solution for sin X = 1/2?

• pi/2 + Npi

• pi/3 + 2Npi

• pi/4 + Npi

• pi/6 + 2Npi

What angle gives a tangent value of 1?

• pi/3

• pi/6

• pi/4

• pi/2

What is the general solution for tan 3X = 1?

• pi/6 + Npi/2

• pi/4 + Npi

• pi/12 + Npi/3

• pi/3 + Npi/4