Questions: If sin(46°) = cos(θ) and 0° < θ < 90°, then θ = □ degrees

Transcript text: If $\sin \left(46^{\circ}\right)=\cos (\theta)$ and $0^{\circ}<\theta<90^{\circ}$, then $\theta=$ $\square$ degrees

Solution

Solution Steps

To solve for $\theta$ given that $\sin(46^\circ) = \cos(\theta)$ and $0^\circ < \theta < 90^\circ$, we can use the complementary angle identity for sine and cosine, which states that $\sin(x) = \cos(90^\circ - x)$. Therefore, $\theta$ can be found by calculating $90^\circ - 46^\circ$.

Step 1: Given Information

We are given the equation $ \sin(46^\circ) = \cos(\theta) $ and the constraint $ 0^\circ < \theta < 90^\circ $.

Step 2: Use the Complementary Angle Identity

Using the identity $ \sin(x) = \cos(90^\circ - x) $, we can rewrite the equation as: \[ \cos(\theta) = \sin(46^\circ) \implies \theta = 90^\circ - 46^\circ \]

Step 3: Calculate $\theta$

Now, we perform the calculation: \[ \theta = 90^\circ - 46^\circ = 44^\circ \]