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6-2 Trigonometry

In today's Trigonometry lesson, we will expand on our understanding of the sine, cosine, and tangent functions by exploring the three key trigonometric identities derived from the Pythagorean theorem. These identities are essential for solving various trigonometric problems effectively. We will practice finding values of trigonometric functions using different identities, including cases where cosecant is given, and determining all six trigonometric functions from a standard position angle. Get ready to deepen your trigonometric skills and solve exciting problems!

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6-2 Trigonometry

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  1. 6-2 Trigonometry Day 2

  2. Yesterday we concentrated on sine, cosine and tangent functions. Today we will focus on the other 3 plus 3 trigonometric identities that you need to know!!!!

  3. Trigonometric Functions r y θ x

  4. Examples • Find • Find • Find

  5. Now the Identities The three identities come from the Pythagorean Theorem. Apply it to the picture above. What do you get? r y θ x

  6. Now divide both sides by r2 Now replace with the trig functions – what do you get?

  7. The First Identity Can we write it as Divide both sides by cos2x. What do you get? Divide by sin2x instead – what happens?

  8. The Identities

  9. Why these? These identities give us a couple of ways to solve problems. • Csc x = 3, x is in Q II. Find the other 5 trig functions. • When θ is put in standard position its terminal side passes through (-5, -12). Find all six trig functions of θ.

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