aiven \( \sin \beta=\frac{8}{c 7} \) where \( 90^{\circ} \leq \beta \leq 270^{\circ} \) dotormine witrad using a calechator a) \( \cos 2 \beta \) b) \( \sin 2 \beta \)

To determine \( \cos 2\beta \) and \( \sin 2\beta \) from the equation \( \sin \beta = \frac{8}{c 7} \), where \( 90^{\circ} \leq \beta \leq 270^{\circ} \), first we need to find the value of \( \beta \). Using a calculator, compute \( \beta = \arcsin\left(\frac{8}{c 7}\right) \). Given the range of \( \beta \), we can determine that it will be in the second or third quadrant, where sine is positive for the second quadrant and negative for the third (but here, we only consider the context that implies \( \sin \) must still yield a valid output based on the calculator's range). Once you've found \( \beta \), apply the double angle formulas: - \( \cos 2\beta = 1 - 2\sin^2\beta \) - \( \sin 2\beta = 2\sin\beta \cos\beta \) From sorting those values out through calculation, you’ll find the numbers to plug into those formulas to get your final answers. Don’t forget the relation \( \cos^2\beta + \sin^2\beta = 1 \) to determine \( \cos \beta \) as well! Time to crunch that calculator!