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Trigonometry Basics: Finding Cosine and Sine, Calculator Tips, Latitude Studies

Learn how to find cosine and sine, use a calculator for trig functions, and calculate latitudes on Earth. Homework questions included.

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Trigonometry Basics: Finding Cosine and Sine, Calculator Tips, Latitude Studies

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  1. The terminal side passes through (1, -2), find cosƟ and sinƟ. • The sine of an angle is . The angle is in Quadrant II. What is the cosine of the angle? • The cosine of an angle is . The angle is in Quadrant IV. What is the sine of the angle? • Solve in radians: cosƟ= 0 Warm Up

  2. Period: Amplitude: 1 Domain: Range: Sine Graph

  3. Period: Amplitude: 1 Domain: Range: Cosine Graph

  4. Simulation of sine and cosine graphs

  5. Locate on your unit circle. How far is from the x-axis? is the reference angle. Locate -240 ̊on your unit circle. How far is -240 ̊from the x-axis? 60 ̊ Reference Angles 60 ̊ is the reference angle.

  6. Reference Angles Find the reference angle for each angle 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 48.4 37 24 3 10 25

  7. Expressing a Trig Expression in Terms of a Reference Angle Ex: Express sin 695 ̊ in terms of a reference angle. 1. Locate the angle on the unit circle. IV 2. What quadrant is it in? Is the sin/cos value positive or negative in that quadrant? Negative 25 ̊ 3. Find the reference angle. 3. Write your answer: sin 695̊ = -sin25 ̊

  8. sin 170 ̊ 2. sin(-15 ̊) 3. sin 400 ̊ 4. cos 160 ̊ 5. cos 182 ̊ 6. cos (-100 ̊) sin 10 ̊ -sin 15 ̊ sin 40 ̊ -cos 20 ̊ Give each of the following in terms of a reference angle. -cos 2 ̊ -cos 80 ̊

  9. Sine and Cosine on the Calculator Before doing any calculations involving trig functions always check the calculator mode. How to use your calculator to find sin  and cos 

  10. Make sure to check the mode then evaluate the expressions below:

  11. The latitude of a point on Earth is the degree measure of the shortest arc from that point to the equator. For example, the latitude of point P in the diagram equals the degree measure of arc PE. Latitude E

  12. The Latitude of Rome is approximately 42N The radius of earth is approximately 3963 miles = 2905 miles How far is Rome from the equator?

  13. The Latitude of Durham is approximately 36 N The radius of earth is approximately 3963 miles Durham is 90 ̊- 36 ̊= 54 ̊ from the North Pole How far is Durham, North Carolina from the North Pole? = 3735miles

  14. Page 279 1-19 odd, 24, 27-31 odd Homework

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