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

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4 Dec 202301:25

Summary

TLDRIn 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.