How to find all the six trigonometric function given a triangle with a radical

The video tutorial covers trigonometric ratios and their application in solving triangle problems. It begins with an introduction to different types of triangles and the Pythagorean theorem. The instructor demonstrates how to apply the theorem to find unknown sides of a triangle, emphasizing the importance of context in problem-solving. The tutorial also explains how to identify and label the sides of a triangle relative to an angle. Finally, it covers the calculation and simplification of trigonometric ratios, including sine, cosine, and tangent, and discusses the characteristics of a 30-60-90 triangle.

What theorem is used to find the unknown sides of a right triangle?

• Pythagorean Theorem

• Law of Sines

• Law of Cosines

• Triangle Inequality Theorem

In the context of the problem, why is only the positive value of the side considered?

• Because the triangle is equilateral

• Because negative values do not make sense for side lengths

• Because the triangle is isosceles

• Because the triangle is scalene

Which side of a triangle is labeled as the hypotenuse?

• The side opposite the largest angle

• The side opposite the smallest angle

• The side adjacent to the right angle

• The side opposite the right angle

What is the cosine of an angle in a right triangle defined as?

• Hypotenuse over Adjacent

• Opposite over Adjacent

• Adjacent over Hypotenuse

• Opposite over Hypotenuse

How can you identify a 30-60-90 triangle based on trigonometric ratios?

• By checking if the sine of the angle is 1

• By checking if the cosine of the angle is 0

• By comparing the ratios to known values of a 30-60-90 triangle

• By ensuring all sides are equal