1. Be sure to attach a hand - sketch for this problem. (a) First draw ????45 in standard position. (b) Now draw the reference angle of ????

1. Be sure to attach a hand - sketch for this problem.

(a) First draw −????45° in standard position.

(b) Now draw the reference angle of −????45° in the same diagram. Do not find the value, just draw it.

Remember the definition: The reference angle of a given angle is the POSITIVE ACUTE angle formed by the terminal side of the angle and the NEAREST x - axis.

(c) Use the drawing in part (b) to find the value of the reference angle.

2. Find the exact value of the following expression which basically stands for the sum of cos1° , cos2° ,cos3° all the way up to cos179°. Do not use a calculator.

cos1° + cos2°+ cos3° + ⋯⋯⋯ + cos178° + cos179°

Hints: See the hints below.

i. Start by establishing a relationship between the last term cos179° and the first term cos1°. To establish the relationship, first draw 179° in standard position and find its reference angle. Then use the reference angle and the quadrant in which 179° lies to rewrite cos179° in terms of cos1°. This will help you evaluate cos1°+ cos179°.

ii. Follow the above method to evaluate the intermediate sums cos2°+ cos178°, cos3° + cos177° and so on.

3. A person's blood pressure follows a sine wave corresponding to the beats of the heart. A particular individual's blood pressure at time t (measured in minutes) is

P (t) = 20 sin(160????????????????) + 110.

What does this tell us about the person's (a) heart rate, (b) systolic and diastolic blood pressure?

4. Determine the amplitude, period, and phase shift for the function ????????= ????????cos(1????????????????− 13 ). Then graph one period of the function using a graphing utility such as Graphmatica, Desmos or something of your choice. Hand sketches will not be accepted.