Solve the equation for solutions in the interval [0 $$\left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$$ ). Round to the nearest degree.
-$\sin 2 \theta + \cos 2 \theta = 1$

Question

Quizplus · Accepted Answer

To solve $\sin 2\theta + \cos 2\theta = 1$, we can use the identity $\sin^2 x + \cos^2 x = 1$. However, this equation involves both sine and cosine functions, so we need to manipulate it. One approach is to express both sine and cosine in terms of either sine or cosine using trigonometric identities, but in this case, it's more straightforward to look for values of $\theta$ that satisfy the given equation within the specified interval. Testing the given options directly or using trigonometric identities and properties to simplify the equation, we find that option D provides the correct set of $\theta$ values that satisfy the equation within the interval $[0^\circ, 360^\circ)$.

Solve the Equation for Solutions in the Interval [0 [0∘,360∘)\left[ 0 ^ { \circ } , 360 ^ { \circ } \right)[0∘,360∘)

Solve the Equation for Solutions in the Interval [0 $\left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$