Mathegoras

Trigonometry › Exact trigonometric values › Exact values

Sine of a difference from given values

High school · ●●●○○ 50 pts

Given that α,β∈(π3,5π6)\alpha, \beta \in \left(\frac{\pi}{3}, \frac{5\pi}{6}\right), if sin⁡(α+π6)=45\sin\left(\alpha + \frac{\pi}{6}\right) = \frac{4}{5} and cos⁡(β−5π6)=513\cos\left(\beta - \frac{5\pi}{6}\right) = \frac{5}{13}, find the value of sin⁡(α−β)\sin(\alpha - \beta). Round to two decimal places.

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Pythagorean identitytrigonometric identities