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Double Angle Identities and Triangle Properties

Double Angle Identities and Triangle Properties

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

The video visually proves two trigonometric double angle identities using a right triangle and its reflection to form an isosceles triangle. It applies the law of sines and the law of cosines to derive the sine and cosine double angle identities. The video concludes by questioning the validity of these identities for obtuse angles.

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9 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the length of the hypotenuse in the initial right triangle?

1

Theta

Pi/2

Sine of Theta

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the complementary angle of Theta in the original triangle?

Pi/2 + Theta

Pi/2 - Theta

2 Theta

Theta

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the angle of the larger isosceles triangle formed by reflecting the original triangle?

2 Theta

Theta/2

Theta

Pi/2

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which law is used to derive the sine double angle identity?

Law of Cosines

Law of Sines

Law of Tangents

Pythagorean Theorem

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the sine double angle identity derived in the video?

sin(2 Theta) = cos^2(Theta)

sin(2 Theta) = 2 sin(Theta) cos(Theta)

sin(2 Theta) = 1 - 2 sin^2(Theta)

sin(2 Theta) = sin^2(Theta)

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which law is applied to derive the cosine double angle identity?

Law of Tangents

Law of Cosines

Law of Sines

Pythagorean Theorem

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the cosine double angle identity derived in the video?

cos(2 Theta) = 1 - 2 sin^2(Theta)

cos(2 Theta) = 2 sin(Theta) cos(Theta)

cos(2 Theta) = 2 cos^2(Theta) - 1

cos(2 Theta) = sin^2(Theta) + cos^2(Theta)

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