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Pre-Calculus PreAP/Dual, Revised ©2014
Basic Trig Identities Section 6.5 Pre-Calculus PreAP/Dual, Revised ©2014 4/26/ :28 AM 6.5 - Basic Trig Identities
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6.5 - Basic Trig Identities
Definition An identity is an equation that is true for all values of the variables for which every term of the equation is defined. An odd function is a function that is symmetrical at the origin An even function is a function that is symmetrical through the y-axis 4/26/ :28 AM 6.5 - Basic Trig Identities
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Reciprocal Identities Theorem
sin θ= csc θ= cos θ= sec θ= tan θ= cot θ= 4/26/ :28 AM 6.5 - Basic Trig Identities
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6.5 - Basic Trig Identities
Quotient Identities 4/26/ :28 AM 6.5 - Basic Trig Identities
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6.5 - Basic Trig Identities
Example 1 Simplify tan t cos t 4/26/ :28 AM 6.5 - Basic Trig Identities
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6.5 - Basic Trig Identities
Example 2 Simplify cos t sec t 4/26/ :28 AM 6.5 - Basic Trig Identities
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6.5 - Basic Trig Identities
Your Turn Simplify csc t tan t 4/26/ :28 AM 6.5 - Basic Trig Identities
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Pythagorean Identities
4/26/ :28 AM 6.5 - Basic Trig Identities
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Pythagorean Identities
4/26/ :28 AM 6.5 - Basic Trig Identities
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Pythagorean Identities
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6.5 - Basic Trig Identities
Example 3 Simplify, tan2t • cos2t + cos2t 4/26/ :28 AM 6.5 - Basic Trig Identities
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6.5 - Basic Trig Identities
Example 4 Simplify, 𝐬𝐢𝐧 𝜽 𝐜𝐨𝐬 𝜽 + 𝐜𝐨𝐬 𝜽 𝟏+𝐬𝐢𝐧 𝜽 4/26/ :28 AM 6.5 - Basic Trig Identities
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6.5 - Basic Trig Identities
Example 5 Simplify, 𝐬𝐞𝐜 𝟐 𝒕− 𝐭𝐚𝐧 𝟐 𝒕 𝐭𝐚𝐧 𝟐 𝒕 4/26/ :28 AM 6.5 - Basic Trig Identities
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6.5 - Basic Trig Identities
Your Turn Simplify, 𝐭𝐚𝐧 𝒕+ 𝐜𝐨𝐭 𝒕 𝐭𝐚𝐧 𝒕 4/26/ :28 AM 6.5 - Basic Trig Identities
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Negative Reciprocal Identity (AKA) Even-Odd Identity
Reflects across the x-axis 4/26/ :28 AM 6.5A - More Trig Identities
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6.5A - More Trig Identities
Definition An odd function is a function that is symmetrical at the origin sin (–t) = –sin t tan (–t) = –tan t An even function is a function that is symmetrical through the y-axis cos (–t) = cos t 4/26/ :28 AM 6.5A - More Trig Identities
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6.5A - More Trig Identities
Example 6 Determine whether f(t) = sin t is an odd or even function. Justify answer. 4/26/ :28 AM 6.5A - More Trig Identities
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6.5A - More Trig Identities
Example 7 Determine whether f(t) = t sin t is an odd or even function. Justify answer. 4/26/ :28 AM 6.5A - More Trig Identities
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6.5A - More Trig Identities
Your Turn Determine whether f(t) = t cos t is an odd or even function. Justify answer. 4/26/ :28 AM 6.5A - More Trig Identities
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6.5A - More Trig Identities
Example 8 Find sin t and tan t when 𝐜𝐨𝐬 𝒕=− 𝟑 𝟏𝟎 within the quadrant in 𝝅<𝒕< 𝟑𝝅 𝟐 4/26/ :28 AM 6.5A - More Trig Identities
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6.5A - More Trig Identities
Example 9 Find sin t, cos t, and tan t when 𝐬𝐞𝐜 𝒕=𝟐 where 𝐬𝐢𝐧 𝒕<𝟎 4/26/ :28 AM 6.5A - More Trig Identities
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6.5A - More Trig Identities
Your Turn Find cos t, and tan t when 𝐬𝐢𝐧 𝒕=− 𝟏 𝟒 where 𝐬𝐞𝐜 𝒕<𝟎 4/26/ :28 AM 6.5A - More Trig Identities
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6.5 - Basic Trig Identities
Assignment Page all, 15, 17, 23, odd all 4/26/ :28 AM 6.5 - Basic Trig Identities
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