# Chapter 5 - Trigonometric Identities - Section 5.3 Sum and Difference Identities for Cosine - 5.3 Exercises - Page 219: 40

$$\theta=69.6^\circ$$

#### Work Step by Step

$$\cos\theta=\sin\Big(\frac{\theta}{4}+3^\circ\Big)\hspace{1cm}(1)$$ We already get from the cofunction identity that $$\cos\theta=\sin(90^\circ-\theta)$$ That means using that in $(1)$, it can lead to $$\sin(90^\circ-\theta)=\sin\Big(\frac{\theta}{4}+3^\circ\Big)$$ $$90^\circ-\theta=\frac{\theta}{4}+3^\circ$$ $$\frac{5\theta}{4}=87^\circ$$ $$\theta=\frac{87^\circ}{\frac{5}{4}}=\frac{87^\circ\times4}{5}$$ $$\theta=69.6^\circ$$

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