4d Warm up

The video tutorial covers the properties of 30-60-90 triangles, focusing on their side ratios and how these relate to the unit circle. It explains how to find missing sides and calculate the sine of 30 degrees. The concept of similar triangles is discussed, emphasizing that the ratios of their sides remain constant. The unit circle is introduced, highlighting its importance in simplifying trigonometric functions when the hypotenuse is 1. The tutorial concludes by explaining how coordinate points on the unit circle relate to trigonometric functions.

What is the relationship between the short leg and the hypotenuse in a 30-60-90 triangle?

• The hypotenuse is half the short leg.

• The hypotenuse is the same as the short leg.

• The hypotenuse is three times the short leg.

• The hypotenuse is twice the short leg.

In a 30-60-90 triangle, if the short leg is X, what is the length of the long leg?

• 2X

• X/2

• X * sqrt(3)

• X * sqrt(2)

Why does the sine of 30 degrees remain consistent across different 30-60-90 triangles?

• Because all 30-60-90 triangles are similar.

• Because the angles are different.

• Because the hypotenuse is always the same length.

• Because all 30-60-90 triangles are congruent.

What is the sine of a 30-degree angle in a 30-60-90 triangle?

• 2/3

• sqrt(3)/2

• 1/2

• 1

Why is it beneficial to use a triangle with a hypotenuse of 1?

• It makes calculations more complex.

• It is a standard size.

• It is easier to draw.

• It simplifies trigonometric calculations.

What does the hypotenuse of 1 in a triangle represent in the context of the unit circle?

• The radius of the circle.

• The diameter of the circle.

• The area of the circle.

• The circumference of the circle.

In the unit circle, what does the Y-coordinate represent?

• The secant of the angle.

• The cosine of the angle.

• The tangent of the angle.

• The sine of the angle.

How is the tangent of an angle represented in the unit circle?

• Y-coordinate multiplied by X-coordinate.

• X-coordinate divided by Y-coordinate.

• Y-coordinate divided by X-coordinate.

• X-coordinate minus Y-coordinate.

What is the primary condition for using the unit circle to simplify trigonometric functions?

• The circle must have a radius of 1.

• The circle must have a radius of 0.5.

• The circle must have a radius of 2.

• The circle must have a radius of 3.

What is the significance of the unit circle in trigonometry?

• It is used to draw perfect circles.

• It simplifies the calculation of trigonometric functions.

• It helps in finding the area of a circle.

• It is used to measure angles in degrees.