The daily average temperature in Santiago, Chile, varies over time in a. periodic way that can be modeled approximately by a trigonometric function. Assume the length of the year (which is the period of change) is exactly 365 days. long. The hottest day of the year, on average, is January 7 , when the average temperature is about \( 29^{\circ} C \). The average temperature at the coolest day of the year is about \( 14^{\circ} C \). Find the formula of the trigonometric function that models the daily average temperature \( T \) in Santiago \( d \) days into the year. ( \( d=1 \) on January 1\( ) \) Define the function using radians.

Without using a calculator, compute the sine and cosine of \( 120^{\circ} \) by using the reference angle. What is the reference angle? \( \square \) degrees. In what quadrant is this angle? \( \square \) (answer \( 1,2,3 \), or 4 )

\begin{tabular}{l} (b) Using the formula \( \operatorname{Sin} 2 A=2 \operatorname{Sin} A \operatorname{Cos} A \) \\ solve the equation \( \sin 2 x-\cos x=0 \) \\ in the interval \( 0^{\circ} \leq x \leq 360^{\circ} \) \\ \hline\end{tabular}

Without using a calculator, compute the sine and cosine of \( 120^{\circ} \) by using the reference angle. What is the reference angle? In what quadrant is this angle? \( \sin \left(120^{\circ}\right)=\square \) degrees. \( \cos \left(120^{\circ}\right)=\square \) (Type sqrt(2) for \( \sqrt{2} \) and sqrt(3) for \( \sqrt{3} \).)

Without using a calculator, compute the sine and cosine of \( \frac{3 \pi}{4} \) by using the refer What is the reference angle? \( \square \) radians. In what quadrant is this angle? \( \sin \left(\frac{3 \pi}{4}\right)=\square \) \( \cos \left(\frac{3 \pi}{4}\right)=\square \)

If \( \sin (\theta)=-\frac{2}{3} \), and \( \theta \) is in quadrant IV, then find (a) \( \cos (\theta)=\square \) (b) \( \tan (\theta)=\square \) (c) \( \sec (\theta)=\square \) (d) \( \csc (\theta)=\square \) (e) \( \cot (\theta)=\square \)