9: Utambulisho wa Trigonometric na Ulinganisho
- Page ID
- 178164
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Katika sura hii, sisi kujadili jinsi ya kuendesha equations trigonometric algebraically kwa kutumia formula mbalimbali na utambulisho trigonometric. Pia tutachunguza baadhi ya njia ambazo equations ya trigonometric hutumiwa kutengeneza matukio halisi ya maisha.
- 9.0: Utangulizi wa Utambulisho wa Trigonometric na Ulinganisho
- Math ni kila mahali, hata katika maeneo ambayo hatuwezi kutambua mara moja. Kwa mfano, mahusiano ya hisabati yanaelezea uhamisho wa picha, mwanga, na sauti. Matukio kama hayo yanaelezwa kwa kutumia equations na kazi za trigonometric. Katika sura hii, sisi kujadili jinsi ya kuendesha equations trigonometric algebraically kwa kutumia formula mbalimbali na utambulisho trigonometric.
- 9.1: Kutatua Ulinganisho wa Trigonometric na Utambulisho
- Katika sehemu hii, tutaanza uchunguzi wa utambulisho wa msingi wa trigonometric, ikiwa ni pamoja na jinsi tunavyoweza kuthibitisha na jinsi tunavyoweza kuitumia ili kurahisisha maneno ya trigonometric.
- 9.2: Utambulisho wa Jumla na Tofauti
- Fomu ya jumla ya cosines inasema kwamba cosine ya jumla ya pembe mbili ni sawa na bidhaa ya cosines ya pembe bala bidhaa ya sines ya pembe. Fomu tofauti ya cosines inasema kwamba cosine ya tofauti ya pembe mbili ni sawa na bidhaa ya cosines ya pembe pamoja na bidhaa ya sines ya pembe. Fomu za jumla na tofauti zinaweza kutumika kupata maadili halisi ya sine, cosine, au tangent ya angle.
- 9.3: Mbili-Angle, Nusu-Angle, na Kupunguza Formula
- Katika sehemu hii, tutachunguza makundi matatu ya ziada ya utambulisho. Utambulisho wa pembeni mbili hutokana na kanuni za jumla za kazi za msingi za trigonometric: sine, cosine, na tangent. Njia za kupunguza ni muhimu hasa katika calculus, kwa vile zinatuwezesha kupunguza nguvu ya muda wa trigonometric. Njia za nusu za angle zinatuwezesha kupata thamani ya kazi za trigonometric zinazohusisha pembe za nusu, ikiwa angle ya awali inajulikana au la.
- 9.4: Jumla ya bidhaa na Bidhaa kwa-Jumla Formula
- Kutoka kwa utambulisho wa jumla na tofauti, tunaweza kupata fomu za bidhaa hadi jumla na fomu za jumla kwa bidhaa kwa sine na cosine. Fomu za bidhaa kwa jumla zinaweza kuandika tena bidhaa za sines, bidhaa za cosines, na bidhaa za sine na cosine kama kiasi cha tofauti za sines na cosines. Tunaweza pia kupata utambulisho wa jumla hadi bidhaa kutoka kwa utambulisho wa bidhaa hadi jumla kwa kutumia mbadala. Fomu za jumla hadi bidhaa hutumiwa kuandika upya jumla au tofauti kama bidhaa za sines na cosines.
- 9.5: Kutatua equations ya Trigonometric
- Katika sehemu za awali za sura hii, tuliangalia utambulisho wa trigonometric. Utambulisho ni kweli kwa maadili yote katika uwanja wa kutofautiana. Katika sehemu hii, tunaanza utafiti wetu wa equations trigonometric kujifunza matukio halisi ya dunia kama vile kutafuta vipimo vya piramidi.