1 / 9

Chapter 6: Trigonometry 6.5: Basic Trigonometric Identities

Chapter 6: Trigonometry 6.5: Basic Trigonometric Identities. Essential Question: What is the Pythagorean Identity? How can it be used to find other trigonometric identities?. 6.5: Basic Trigonometric Identities. Convert to radian mode for this section 2 nd → more Parenthesis matter

salena
Download Presentation

Chapter 6: Trigonometry 6.5: Basic Trigonometric Identities

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Chapter 6: Trigonometry6.5: Basic Trigonometric Identities Essential Question:What is the Pythagorean Identity? How can it be used to find other trigonometric identities?

  2. 6.5: Basic Trigonometric Identities • Convert to radian mode for this section • 2nd → more • Parenthesis matter • “cos (x + 3)” and “cos x + 3” yield different results • Why? • (cos t)2 is written (on paper) as cos2 t, because we’re squaring the result of the cosine function, not the “t”

  3. 6.5: Basic Trigonometric Identities • Quotient Identities • Example 1: Simplify the expression: tan t cos t • The key for conversion is to get everything in terms of sin and cos.

  4. 6.5: Basic Trigonometric Identities • Reciprocal Identities • We’ve seen these before • Example 2: Reciprocal Identities • Given that sin t = 0.28 and cos t = 0.96. Find csc t and sec t

  5. 6.5: Basic Trigonometric Identities • Pythagorean Identities • You know the traditional, a2 + b2 = c2 • sin2 t + cos2 t = 1 • The other two identities can be derived from this equation • tan2 t + 1 = sec2 t • 1 + cot2 t = csc2 t • Example 3: Using Pythagorean identities • Simplify the equation: tan2 t cos2 t + cos2 t • Rewrite using just sin & cos

  6. 6.5: Basic Trigonometric Identities • Example 4: Finding all other values from one • The value for trigonometric function is given for 0 < t < π/2. Use quotient, reciprocal and Pythagorean identities to find the other values of the remaining five trigonometric functions. Round your answers to four decimal places. • sec t = 2.5846 cos t = ? • csc t = ? sin t = ? • cot t = ? tan t = ?

  7. 6.5: Basic Trigonometric Identities • sec t = 2.5846 cos t = 0.3869 • csc t = ? sin t = ? • cot t = ? tan t = 2.3833 • cos can be found as it’s the reciprocal of sec • cos t = 1/sec t = 1/2.5846 = 0.3869 • tan can be found with the Pythagorean theorem • sec2 t = tan2 t + 1 • 2.58462 – 1 = tan2 t • 2.3833 = tan t

  8. 6.5: Basic Trigonometric Identities • sec t = 2.5846 cos t = 0.3869 • csc t = 1.0850 sin t = 0.9217 • cot t = 0.4199 tan t = 2.3833 • cot can be found as it’s the reciprocal of tan • cot t = 1/tan t = 1/2.3833 = 0.4199 • tan t = sin t / cos t • 2.3833 = sin t / 0.3896 • 2.3833 ● 0.3896 = sin t • 0.9217 = sin t • csc can be found by taking the reciprocal of sin • csc t = 1/sin t = 1/0.9217 = 1.0850

  9. 6.5: Basic Trigonometric Identities • Assignment • Page 460 • 1 – 25, odd problems • Show work

More Related