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Inverse Functions for sin θ, cos θ, tan θ, cot θ, sec θ, & csc θ

Learn how to find the inverse functions for trigonometric ratios such as sine, cosine, tangent, cotangent, secant, and cosecant. Understand the process of taking the inverse, and practice solving for angles in degrees or radians.

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Inverse Functions for sin θ, cos θ, tan θ, cot θ, sec θ, & csc θ

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  1. Got ID? 2-7-19 T2.1e To Find the Inverse Functions for sin Ө, cos Ө, tan Ө cot Ө, sec Ө, & csc Ө “It’s an obstacle illusion” –Alan-Edward Warren—Sr. 2014

  2. Active Learning Assignment Questions?

  3. 2 1 LESSON: To find the inverse for sin Ө , cos Ө , and tan Ө. This is written as Sin-1, Cos-1, and Tan-1. It can also be written as Arcsin, Arccos, and Arctan. These two terms are INTERCHANGEABLE!!!!!!!! If sin Ө = ratio, and we know the angle, we can find the ratio. (Put your calculator back in degrees.) Ex: sin 30° = xJust use your calculator (or build the triangle to find it). 0.5 = x

  4. How do we get Ө by itself? BUT, what if we know the ratio, but want to solve for the angle (in degrees)? Start with: We take the sine inverse of both sides! (Pronounced sine inverse) Put a RATIO into the inverse function. Since Sin-1 inverses sin, this is all we have left. Get an ANGLE out! Now, we use the calculator (see 2nd function above sin).

  5. Ө Inverse functions must pass both the vertical line test and the horizontal line test because when we take the inverse, we switch the domain and range (the ratio becomes the questions (x) and the angle becomes the answer (y)) ratio Ө ratio Ө ratio Ө ratio Ө ratio Ө ratio

  6. II I III IV * Positive and Negative Quadrants for Inverse Functions * = 60° All positive in QI 90° = 30° = 120° 180° 0° = -30° * * -90° * (Reciprocals go together, too.)

  7. Radian vs. Degree. What is the difference between these two? in degrees in radians You cannot tell by the expression. You must receive instructions as to which one is needed. Once that is established, just change your calculator to the appropriate setting. Let’s try to find it in radians. In radians, to four decimal places. Same as = 1.1681

  8. Try these: Try: Ө Either Degrees or Radians ratio Degrees, 2 dec. pl. Degrees, 2 dec. pl. Radians, 4 dec. pl. 16.26° 124.75° 0.9273 Error! Error! Error!

  9. To solve for Ө , we use the reciprocal property for csc Ө What about Sec-1 x , Csc-1 x , and Cot-1 x ? It’s the same process, except for changing the function to it’s reciprocal. Given, find in degrees: Flip that equation! Inverse both sides Simplify The same! Solve, in degrees, two decimal places.

  10. Try: Radians, 4 dec. pl. Degrees, 2 dec. pl.

  11. Active Learning Assignment: P 289: Written Exercises 1 – 4 Find each in degrees (2 dec. pl.). (Make sure your calculator is in degrees) 1. cot Ө = 5.829 2. cscӨ = 3 3. sec Ө = (-1.8726) 4. sec Ө = 2.8 5. cscӨ = 8.29 6. cot Ө = 0.75 TEST on T2.1a, T2.1c, T2.1d, T2.1e & T2.1f on Tuesday, 2-12-19 AND (Answers to these six are on the next page.)

  12. Answers for 1 – 6 on previous page: In Degrees: 1. 9.73° 2. 19.47° 3. 122.28° 4. 69.08° 5. 6.93° 6. 53.13°

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