The Inverse Cosine Function Lesson 5.3. Reminder… y = cos x.

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Presentation transcript:

The Inverse Cosine Function Lesson 5.3

Reminder… y = cos x

y = cos -1 x If we took y = cos x on its entire domain, the inverse would not be a function So, we restrict the domain of cos -1 x to 0 ≤ y≤ π Different calculators  cos -1 x = arccos = acos

Reminder… y = cos x

Example 1 Evaluate arccos (1/2), giving an answer in radians. arccos(1/2) = x cos x = ½ (between 0 and π) x = 60˚ So π/3

Example 2 Find the exact value of cos -1 Cos x = (between 0 and π) x = 135˚ or 3π/4

Example 3 Evaluate cos -1 ( ) to the nearest degree. x = 7˚

Example 4 Find the cos (cos -1 (1/2)) cos (60) 1/2 Find the cos -1 (cos(-30˚)) cos -1 ( ) 30

Homework Pages 325 – – 12, 15, 16 (skip 4 a and b)