Trigonometric Functions and Reference Triangles

The video tutorial explains how to find the sine of u divided by two using the half-angle identity. It starts by setting up a reference triangle in quadrant four to determine the cosine of angle u. The Pythagorean theorem is used to calculate the cosine value. Then, the half-angle identity is applied to find the sine of u divided by two, considering the angle's position in quadrant two. The tutorial concludes with a summary of the steps taken.

What is the given value of sine u in the problem?

• -0.774968

• 0.774968

• -0.632

• 0.632

Tags

CCSS.HSF.TF.A.2

In which quadrant is angle u located?

• Quadrant 1

• Quadrant 2

• Quadrant 3

• Quadrant 4

Tags

CCSS.HSG.SRT.C.6

What is the purpose of using a reference triangle in this problem?

• To find the cosine of u

• To determine the sine of u

• To find the hypotenuse

• To calculate the tangent of u

Tags

CCSS.HSF.TF.A.2

What is the value of y in the reference triangle?

• -0.632

• 0.632

• 1

• -1

Tags

CCSS.HSG.SRT.C.8

Which theorem is used to find the length of the adjacent side in the reference triangle?

• Tangent Rule

• Pythagorean Theorem

• Cosine Rule

• Sine Rule

Tags

CCSS.HSF.TF.A.2

What is the approximate value of x, the adjacent side, in the reference triangle?

• 0.3354

• 1

• 0.774968

• 0.632

Tags

CCSS.HSF.TF.C.9

In which quadrant does the angle u/2 lie?

• Quadrant 1

• Quadrant 4

• Quadrant 2

• Quadrant 3

Tags

CCSS.HSF.TF.C.9

What is the sign of sine of u/2 based on its quadrant?

• Negative

• Undefined

• Zero

• Positive

Tags

CCSS.HSF.TF.C.8

What is the formula used to calculate sine of u/2?

• Tangent Identity

• Cosine Rule

• Half-Angle Identity

• Sine Rule

Tags

CCSS.HSF.TF.C.9

What is the final calculated value of sine of u/2 rounded to four decimal places?

• 0.5

• 0.3354

• 0.774968

• 0.632

Tags

CCSS.HSF.TF.C.9