How to Prove Sin(x/2) = +/- √((1 – cosx) / 2): A Step-by-Step Guide
sin(x/2) = +/- √((1 – cosx) / 2) 1 To prove that sin(x/2) = +/- √((1 – cosx) / 2), we can use the half-angle formula for...
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John Rhodes
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June 21, 2023
Proving the Identity: Simplifying Cosine using Half-Angle and Double-Angle Formulas.
cos(x/2) = +/- √((1 + cosx) / 2) 1 To prove the given identity: We can use the half-angle formula for cosine, which states that cos(x/2) =...
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John Rhodes
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June 21, 2023
Half-Angle Identity for Tangent: Proof and Formula
tan(x/2) = +/- √((1 – cosx) / (1 + cosx)) 1 The identity you provided is known as the half-angle identity for tangent. It states that for...
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John Rhodes
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June 21, 2023
Simplifying sin(α)cos(β) + sin(β)cos(α) using the sine of the sum of two angles identity
sin(α)cos(β) + sin(β)cos(α) 1 The expression sin(α)cos(β) + sin(β)cos(α) is known as the sine of the sum of two angles identity. We can use the following steps...
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John Rhodes
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June 21, 2023
Finding the Point of Tangency: Using Numerical Methods to Solve for x with Specific Slope
The derivative of a function f is given by f′(x)=0.1x+e^0.25x. At what value of x for x>0 does the line tangent to the graph of f at...
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John Rhodes
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June 21, 2023
Calculating Approximate and Actual Derivative Values for f(x)=2x^3 – Method and Results
Let f be the function given by f(x)=2×3. Selected values of f are given in the table above. If the values in the table are used to...
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John Rhodes
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June 21, 2023
Exploring Properties of a Degree 7 Polynomial Function: Real Root Existence and End Behavior.
Let f be the function given by f(x)=(1/7)x^7+12x^6−x^5−(15/4)x^4+(4/3)x^3+6x^2. Which of the following statements is true? f′(0.4)
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John Rhodes
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June 21, 2023
Calculating the Average Rate of Change of a Function f(x) Over a Specified Interval [0,π]
The function f is given by f(x)=1+3cosx. What is the average rate of change of f over the interval [0,π] ? -6/πThe difference quotient [f(π)−f(0)]/(π−0) is the...