- Sin 0 = 0
- Sin pie/ 6 = 1/2
- Sin pie/4 = square root of 2/2
- Sin pie/3 = square root of 3/2
- Sin pie/ 2 = 1
- Cos 0 = 1
- Cos pie/6 = square root of 3/2
- Cos pie/4 = square root of 2/2
- Cos pie/3 = 1/2
- Cos pie/2 = 0
- Csc 0 = 0 undefined
- Csc pie/6 = 2
- Csc pie/4 = square root of 2
- Csc pie/3 = 2 square root of 3/2
- Csc pie/2 = 1
- Sec 0 = 1
- Sec pie/6 = 2 square root of 3/2
- Sec pie/4 = square root of 2
- Sec pie/3 = 2
- Sec pie/2 = undefined
- Tan 0 = 0
- Tan pie/6 = square root of 3/3
- Tan pie/4 = 1
- Tan pie/3 = square root of 3
- Tan pie/2 = undefined
- Cot 0 = undefined
- Cot pie/6 = square root of 3
- Cot pie/4 = 1
- Cot pie/3 = square root of 3/3
- Cot pie/2 = 0
Chapter 10 formulas:
Chapter 10
-cos(alpha plus or minus beta) = cos(alpha)cos(beta) minus or plus sin(alpha)sin(beta)
-sin(alpaha plus or minus beta)= sin(alpha)cos(beta) plus or minus cos(alpha)sin(beta)
-tan(alpha+beta) = tan(alpha + beta)/1-tan(alpha)tan(beta)
-tan(alpha-beta) = tan(alpha-beta)/1+tan(alpha)tan(beta)
-sin2(alpha)= 2sin(alpha)cos(alpha)
-cos2(alpha)= cos^2(alpha)-sin^2(alpha)
-cos2(alpha)= 1-2sin^2(alpha)
-cos2(alpha)= 2cos^2(alpha)-1
-tan2(alpha)= 2tan(alpha)/1-tan^2(alpha)
-sin(alpha)/2= plus or minus square root of 1-cos(alpha)/2
-cos(alpha)/2= plus or minus square root of 1+cos(alpha)/2
-tan(alpha)/2= plus or minus square root of 1-cos(alpha)/1+cos(alpha)
-tan(alpha)/2= sin(alpha)/1+cos(alpha)
-tan(alpha)/2= 1-cos(alpha)/sin(alpha)
-cos(alpha plus or minus beta) = cos(alpha)cos(beta) minus or plus sin(alpha)sin(beta)
-sin(alpaha plus or minus beta)= sin(alpha)cos(beta) plus or minus cos(alpha)sin(beta)
-tan(alpha+beta) = tan(alpha + beta)/1-tan(alpha)tan(beta)
-tan(alpha-beta) = tan(alpha-beta)/1+tan(alpha)tan(beta)
-sin2(alpha)= 2sin(alpha)cos(alpha)
-cos2(alpha)= cos^2(alpha)-sin^2(alpha)
-cos2(alpha)= 1-2sin^2(alpha)
-cos2(alpha)= 2cos^2(alpha)-1
-tan2(alpha)= 2tan(alpha)/1-tan^2(alpha)
-sin(alpha)/2= plus or minus square root of 1-cos(alpha)/2
-cos(alpha)/2= plus or minus square root of 1+cos(alpha)/2
-tan(alpha)/2= plus or minus square root of 1-cos(alpha)/1+cos(alpha)
-tan(alpha)/2= sin(alpha)/1+cos(alpha)
-tan(alpha)/2= 1-cos(alpha)/sin(alpha)
Example 1:
Find the exact value of sin 15 degrees
Sin(45-30) = Sin45 Cos30 - Cos45 Sin30
(square root of 2/2)(square root of 3/2) - (square root of 2/2)(1/2)
= square root of 6/4 - square root of 2/4
= square root of 6 - square root of 2/ 4
Step1) Find out which formula you have to use
Step2) The formula you have to use is sin(alpaha plus or minus beta)= sin(alpha)cos(beta) plus or minus cos(alpha)sin(beta)
Step3) Find out to terms on the trig chart that will subtract to give you 15
Step4) After you find these terms (45 & 30) plug them into your formula as alpha and beta
* The first term is always alpha and the second one is beta
Step5) Find the exact value of the terms according to the trig chart
Step6) Multiply and subtract to find your final answer
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