Calculus | Senioritis

John Rhodes
June 21, 2023
Calculus

Proving Trigonometric Identity: sin^2(x) = (1 – cos^2(2x)) / 2 using Trigonometric Identities

sin^2(x) = (1 – cos^2(2x)) / 2 1 To prove that sin^2(x) = (1 – cos^2(2x)) / 2, we will use the following trigonometric identities. 1. cos(2x)...

John Rhodes
June 21, 2023
Calculus

Proving the Identity: Cos^2(x) = (1 + Cos(2x)) / 2.

cos^2(x) = (1 + cos(2x)) / 2 1 To prove this identity, we can start with the double-angle identity: cos(2x) = cos^2(x) – sin^2(x) We can rearrange...

John Rhodes
June 21, 2023
Calculus

Proving the Trigonometric Identity: tan^2(x) = (1 – cos(2x)) / (1 + cos(2x)) using Double-Angle and Pythagorean Identities

tan^2(x) = (1 – cos(2x)) / (1 + cos(2x)) 1 To prove the identity: tan^2(x) = (1 – cos(2x)) / (1 + cos(2x)), we will use the...

John Rhodes
June 21, 2023
Calculus

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...

John Rhodes
June 21, 2023
Calculus

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) =...

John Rhodes
June 21, 2023
Calculus

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...

John Rhodes
June 21, 2023
Calculus

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...

John Rhodes
June 21, 2023
Calculus

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...