Trigonometric Conversions and Evaluations

Find tanθ if sinθ = √10/10 and cosθ = 5√10/5

• √10/10
• √5/5
• 10/√10
• 5√10/10

Convert the angle in radians to degrees: 17π/4

• 360 degrees
• 540 degrees
• 900 degrees
• 765 degrees

Find the exact value of the expression: 2 sin 5π/4 + 4 tan 5π/6

• -√2 - 4√3/3
• 2√2 - 4√3/3
• -√2 + 4√3/3
• √2 + 4√3/3

Convert 70°15'21" to a decimal in degrees. Round the answer to four decimal places

• 70.5000
• 70.1500
• 70.2558
• 71.0000

Sophia is designing a Ferris wheel that mimics the properties of the unit circle. The Ferris wheel has a radius of 1 meter, and its center is located at the origin (0,0) of a coordinate plane. A single seat moves around the Ferris wheel, starting at the point (1,0).

If the seat rotates counterclockwise by an angle of π/3​ radians, what are the coordinates of the seat on the Ferris wheel?

• (1/2,√3/2)

• (√3/2,1/2)

• (0, 1)
• (1, 0)

Liam is hiking up a hill and stops at a triangular rock formation. The rock formation is a perfect right triangle with the following features:

• The height of the triangle is 4 units.

• The base of the triangle is 3 units.

• The hypotenuse is the side opposite the right angle.

1. What are the exact values of the sine, cosine, and tangent of the angle at the base of the triangle where the height meets the base?

• sinθ=4/5 ​,cosθ=​3/5 ,tanθ=4/3​

• sinθ=3/5 ​,cosθ=4/5 ,tanθ=3/4

• sinθ=4/4 ​,cosθ=3/3 ,tanθ=4/3

• sinθ=​4/6,cosθ=3/6,tanθ=4/6

tan 17π/6

• -1/√3
• -√3
• 1/√3
• 0

sin-17π/4

• -√2/2
• 0
• -1
• √2/2

• Ella is studying the motion of ocean waves for her science project. She observes that the height of the waves can be modeled by the function:

  h(t)=3sin(π/4t)

  where:

  • h(t) represents the height of the wave (in meters) above the average sea level at time t (in seconds).

  • The coefficient 3 represents the maximum height deviation from the average sea level.

  • The term π/4t represents the angular frequency of the wave.

  1. What is the amplitude of the wave?

  2. What is the period of the wave?

• A=3 meters , P=8 seconds

• A=8 meters, P=3 seconds

• A=2 meters, P=7 seconds

• A= 7 meters, P= 2 seconds

Use even-odd properties to locate the value of the expression: sec(90°)

• undefined
• 1
• 0
• infinity