Lesson 4.2

Trigonometric Functions on the Unit Circle

Lesson Overview:

Convert degree measures of angles to radian measures, and vice versa.

QRS:

Quadrant: Find the Quadrant of where it belongs

Reference Angle: Find the reference angle for the original angle

Sign: Find the sign (positive or negative)

Convert degree measures of angles to radian measures, and vice versa

Here is a practice problem for lesson 4.2. In these problems we will use the QRS Method to solve.

Steps:

1. First we have to find the co-terminal angle that is between 0 and 360 degrees.
2. Then we use our QRS method (Quadrant, Reference Angle, Sign). This step is very important and helps us find our final answer.
3. By using our left hand trigonometry skills learned in lesson 4.1, we can solve for the final answer. Make sure to always include the sign!

Real World Application:

On February 10, 1990, high tide in Boston was at midnight. The water level at high tide was 9.9 feet; later, at low tide, it was 0.1 feet. Assuming the next high tide is exactly 12 hours later and that the height of the water is given by a sine or cosine curve, find a formula for water level in Boston as a function of time.

Suppose the height of the water level is y feet, and let t be the time measured in hours from midnight.
Then the oscillations are to have amplitude 4.9 feet (=(9.9-0.1)/2) and period 12, so 12b = 2 and b.=./6.
Since the water is highest at midnight, when t.=.0, the oscillations are best represented by a cosine function, because the cosine is at its maximum at the beginning of the cycle. Thus we can say the height above average = 4.9cos(t/6)
Since the average depth of the water was 5 feet (= (9.9+0.1)/2), we want the cosine curve shifted up by 5. We get this by adding 5: y = 5 + 4.9cos(t/6).

SAT Prep Question

Triangle ABC is a right triangle with its right angle at B. Therefore, AC is the hypotenuse of right triangle ABC, and AB and BC are the legs of right triangle ABC. According to the Pythagorean theorem,
AB=√(202)−(162)=√(400)−(256)=√144=12
Since triangle DEF is similar to triangle ABC, with vertex F corresponding to vertex C, the measure of angle F equals the measure of angle C. Therefore, sin‌F=sin‌C.
The final answer is 3/5 or 0.6.

Google Sites

Report abuse