If alpha and beta are fourth quadrant angle such that sin alpha = 3 / 5 and sec beta = 17 / 15, ...

Question:

If {eq}\alpha \ and \ \beta {/eq} are fourth quadrant angle such that {eq}\sin \alpha = \frac{3}{ 5} {/eq} and {eq}\sec \beta = \frac{17 }{15}{/eq}, then find {eq}\sin (\alpha - \beta). {/eq}

Trigonometry Problem:

We have to find the value of {eq}\sin (\alpha - \beta) {/eq} where {eq}\alpha \ and \ \beta {/eq} are fourth quadrant angle.We will use the Pythagorean formula for sines and cosines to find the values. Then, substitute the values into difference formulas for sine to get the desired result.

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Use the Pythagorean formula for sines and cosines. So, we have \begin{align*} \sin \alpha &= \frac{3}{5}\\ \cos \alpha &= \sqrt {1 - {{\left(...

Proving the Addition & Subtraction Formulas for Sine, Cosine & Tangent

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Chapter 18 / Lesson 5
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