Mastering 2D Trigonometry Concepts

What is the sine ratio of a 30-degree angle?

• 0.5

• 0.75

• 1.0

• 0.25

If a right triangle has one angle of 45 degrees, what are the lengths of the sides if the hypotenuse is 10?

• Each leg is 7, approximately 9.9.

• Each leg is 5√2, approximately 7.07.

• One leg is 5, the other is 10.

• Each leg is 10, approximately 14.14.

Graph the sine function for one complete cycle from 0 to 2π.

• The graph of the sine function from 0 to 2π is a wave that starts at (0,0), peaks at (π/2,1), crosses the x-axis at (π,0), reaches a minimum at (3π/2,-1), and returns to (2π,0).

• The graph oscillates between (0,0) and (2π,1) without crossing the x-axis.

• The sine function peaks at (π,1) and has a minimum at (π/2,-1).

• The graph of the sine function is a straight line from (0,0) to (2π,0).

What is the cosine of a 60-degree angle?

• 0.25

• 0.866

• 0.5

• 1.0

Using the Pythagorean theorem, find the length of the hypotenuse if the other two sides are 3 and 4.

• 7

• 6

• 5

• 8

What is the tangent ratio of a 45-degree angle?

• 1

• 1/2

• √2

• 0

Identify the coordinates of the point on the unit circle at 90 degrees.

• (0, 1)

• (0, -1)

• (-1, 0)

• (1, 0)

If the opposite side of a right triangle is 5 and the hypotenuse is 13, what is the sine of the angle?

• 5/10

• 12/13

• 5/13

• 3/13

Graph the cosine function for one complete cycle from 0 to 2π.

• The graph of the cosine function starts at (0,0) and ends at (2π,0).

• The graph of the cosine function is a straight line from (0,1) to (2π,1).

• The graph of the cosine function has peaks at (π/4,1) and (5π/4,1).

• The graph of the cosine function from 0 to 2π is a wave starting at (0,1), reaching (π/2,0), (π,-1), (3π/2,0), and returning to (2π,1).

What is the value of sin(π/6)?

• 1/2

• 0

• √3/2

• 1/4