4.2 Now use the results obtained in 4.2 and 4.3 above and circle the correct relationship. In general for any magnitude of \( 0^{\theta}<90^{\theta} \) will: \( 4.1 \sin (-\theta)=\sin \theta \) or \( -\sin \theta \) \( 4.2 \cos (-\theta)=\cos \theta \) or \( -\cos \theta \) \( 4.3 \tan (-\theta)=\tan \theta \) or \( -\tan \theta \)

When dealing with trigonometric functions, it’s helpful to remember that the sine function is an odd function, which means \(\sin(-\theta) = -\sin(\theta)\). This is different from the cosine function, which is an even function, so \(\cos(-\theta) = \cos(\theta)\). Lastly, the tangent function is also odd, revealing that \(\tan(-\theta) = -\tan(\theta)\). So, in summary, for any angle \( 0^{\theta}<90^{\theta} \): 1. \(\sin(-\theta) = -\sin(\theta)\) 2. \(\cos(-\theta) = \cos(\theta)\) 3. \(\tan(-\theta) = -\tan(\theta)\) Understanding these relationships is essential in your mathematical toolkit, and using them will simplify many calculus and geometry problems!