Diketahui cos x=5/13. Nilai dari sin 1/2 x=. . . .

Summary

In this video, the presenter explains how to determine the value of sin(1/2x) using the given value of cos(x) equal to 5/13. The formula for sin(1/2α) is discussed, highlighting the process of substituting the cosine value into the equation. The calculation leads to the expression ±√(4/13), which simplifies to ±(2/√13). Rationalizing this results in ±(2√13/13). The video concludes by confirming that the correct options are -2√13/13 and +2√13/13, engaging viewers with a clear mathematical explanation.

Takeaways

• 😀 The script discusses the determination of the sine value based on the cosine value given.
• 😀 It is specified that cos(x) is equal to 5/13.
• 😀 The formula for sin(1/2 Alpha) is derived as ±√(1 - cos(Alpha)/2).
• 😀 Substituting cos(x) into the formula yields sin(1/2 x) = ±√(1 - 5/13)/2.
• 😀 The calculation simplifies to ±√((13 - 5)/13)/2.
• 😀 Further simplification results in ±√(8/13)/2.
• 😀 This leads to the expression ±(2/√13).
• 😀 The value is then rationalized to ±(2√13/13).
• 😀 The correct options identified are -2√13/13 and +2√13/13.
• 😀 The video concludes with a prompt for the next video explanation.

Q & A

What is the formula for finding sin(1/2x) given cos(x)?

The formula for sin(1/2x) is ±√((1 - cos(x))/2).

What value of cos(x) is used in the calculation?

The value of cos(x) used in the calculation is 5/13.

How is the substitution of cos(x) applied in the formula?

By substituting cos(x) = 5/13 into the formula, we get sin(1/2x) = ±√((1 - 5/13)/2).

What is the result of the substitution step in the formula?

The substitution yields sin(1/2x) = ±√((8/13)/2) = ±√(4/13).

What simplification is performed on √(4/13)?

The simplification involves extracting √4 from the square root, resulting in sin(1/2x) = ±(2/√13).

What is the final rationalized form of sin(1/2x)?

The final rationalized form is ±(2√13/13).

What are the possible values of sin(1/2x)?

The possible values of sin(1/2x) are -2√13/13 and +2√13/13.

What concept does this calculation illustrate in trigonometry?

This calculation illustrates the relationship between sine and cosine functions, particularly using the half-angle formula.

Why is there a plus-minus sign in the final result?

The plus-minus sign indicates that sine can have both positive and negative values depending on the angle x.

What is the significance of the values found in this calculation?

The values help determine the sine of half of the angle x, which is important for solving various trigonometric problems.