Mastering 2D Trigonometry

What is the length of the hypotenuse in a right triangle with legs of lengths 3 and 4?

• 5

• 6

• 8

• 7

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

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

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

• 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.

If angle A in a right triangle is 30 degrees and the adjacent side is 5 units, what is the length of the opposite side?

• 3.5

• 6.0

• 4.0

• 1.732

Using the Pythagorean theorem, find the length of the third side of a triangle with sides 6 and 8.

• 10

• 12

• 14

• 16

Apply the sine rule to find the missing angle in a triangle where sides a=7, b=10, and angle A=30 degrees.

• 60 degrees

• 90 degrees

• 45.57 degrees

• 75 degrees

Calculate the distance between two points (3, 4) and (7, 1) using the distance formula.

• 5.0

• 3.605551275463989

• 4.47213595499958

• 2.8284271247461903

If angle B in a triangle is 45 degrees and side a=10, use the cosine rule to find side c.

• √(100 + 100√2)

• √(200 - 100√2)

• √(300 - 200√2)

• √(150 - 50√2)

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

• The graph of the cosine function reaches its lowest point at (π,1) and highest at (2π,-1).

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

• 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).

In a right triangle, if one angle is 60 degrees and the hypotenuse is 12, what is the length of the adjacent side?

• 8

• 6

• 10

• 4

Using the cosine rule, find the length of side a in a triangle with sides b=5, c=7, and angle A=60 degrees.

• 6.244

• 8.200

• 7.500

• 5.000