Question

In Exploration 4.1.1 problem 3 pre calc

Answer 1

The reference triangle is a right triangle and therefore, the properties of

the reference triangle are similar to right triangle properties.

The correct options are as follows;

• The reference triangle always have a leg perpendicular to the x-axis, the hypotenuse is positive, and θ is the angle adjacent to the x-axis and hypotenuse.

Reasons

The reference triangle is formed by the construction of a perpendicular

to the x-axis from the terminal side of an angle, oriented in the standard

position.

Therefore;

• The reference triangle is a right triangle that always has a leg perpendicular to the x-axis.

• The hypotenuse is taken as positive, given that the magnitude of the hypotenuse is the square root of the sum of the squares of the legs.

• In the first quadrant, the reference angle, θ, is the same as the standard position angle and it is given by the angle formed between the x-axis and the hypotenuse side.

The correct options are therefore;

In Trigonometry it is important that the right triangle (reference triangles)

have a consistent orientation. The reference triangles always have a leg

perpendicular to the x-axis, the hypotenuse positive and the θ is

adjacent to the x-axis and hypotenuse.

Learn more about reference angles and right triangles here:

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