sincos 5 θθ−= ，試求下列各式之值： (1) sin cosθθ⋅ (2)sin cosθθ+ (3)sin cos. 33. 13 ； 12 13 ； 5 12 2、(1)36；(2) 12 5 − 3、36 4、(1) 9 4 ；(2)1 5、 51+ 6、8 7、2 8、 If∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B. Sol. Let us consider a right ΔABC, right-anlged at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P. PR + QR = 25 cm. and PQ = 5 cm. Let QR = x cm Chapter 13 - Surface Areas and Volumes IdentitasTrigonometri 1. Jumlah dan Selisih Dua Sudut a) sin (A + B) = sin A cos B + cos A sin B b) sin (A - B ) = sin A cos B - cos A s Dikuadran pertama, nilai sinus, cosinus, dan tangen bernilai positif. Sedangkan di kuadran kedua, hanya nilai sinus yang bernilai positif. Dalam segitiga siku-siku, jika diketahui panjang 2 sisi, maka sisi yang satunya lagi dapat ditentukan dengan teorema pyhtagoras. Matematika Diketahui cos A = -4/5 dan sin B = 5/13, sudut A d EC Edwin C 15 November 2021 13:19 Pertanyaan Diketahui cos A = -4/5 dan sin B = 5/13, sudut A dan B tumpul. Hitunglah nilai sin ( A+B ) dan sin ( A-B ) 5rb+ 2 Jawaban terverifikasi Iklan Iklan AA Acfreelance A 07 Desember 2021 00:48 Jawaban terverifikasi Jawaban Diketahui : cos a = 3/5 dan sin b = 5/13. jika a sudut lancip dan b sudut tumpul. Ditanya : tentukan nilai dari \sin (\alpha-\beta) ! sin(α−β)! Pembahasan : \cos a=\frac {3} {5}=\frac {samp} {mir} cosa = 53 = mirsamp maka \sin a=\frac {dep} {mir}=\frac {4} {5} sina = mirdep = 54. depan=\sqrt {5^2-3^2}=\sqrt {16}=4 depan = 52 −32 . Given as sin A = 4/5 and cos B = 5/13 As we know that cos A = √1 – sin2 A and sin B = √1 – cos2 B, where 0 < A, B < π/2 Therefore let us find the value of sin A and cos B cos A = √1 – sin2 A = √1 – 4/52 = √1 – 16/25 = √25 – 16/25 = √9/25 = 3/5 sin B = √1 – cos2 B = √1 – 5/132 = √1 – 25/169 = √169 – 25/169 = √144/169 = 12/13 i sin A + B As we know that sin A +B = sin A cos B + cos A sin B Therefore, sin A + B = sin A cos B + cos A sin B = 4/5 × 5/13 + 3/5 × 12/13 = 20/65 + 36/65 = 20 + 36/65 = 56/65 ii cos A + B As we know that cos A +B = cos A cos B – sin A sin B Therefore, cos A + B = cos A cos B – sin A sin B = 3/5 × 5/13 – 4/5 × 12/13 = 15/65 – 48/65 = -33/65 iii sin A – B As we know that sin A – B = sin A cos B – cos A sin B Therefore, sin A – B = sin A cos B – cos A sin B = 4/5 × 5/13 – 3/5 × 12/13 = 20/65 – 36/65 = -16/65 iv cos A – B As we know that cos A - B = cos A cos B + sin A sin B Therefore, cos A - B = cos A cos B + sin A sin B = 3/5 × 5/13 + 4/5 × 12/13 = 15/65 + 48/65 = 63/65 $\begingroup$I've used the angle sum identity to end up with $\cos A \cos B -\sin A \sin B = \frac{5}{13} = \frac{3}{5}\cos B -\frac{4}{5} \sin B$, but don't know how to proceed from here. Any tips? asked Aug 10, 2017 at 1020 $\endgroup$ 1 $\begingroup$Hint $\cos B=\cosA+B-A$ use the compound angle formula answered Aug 10, 2017 at 1029 David QuinnDavid gold badges19 silver badges48 bronze badges $\endgroup$ $\begingroup$ $$A=\arcsin\dfrac45=\arccos\dfrac35$$ $$A+B=\arccos\dfrac5{13}=\arcsin\dfrac{12}{13}$$ $$B=\arccos\dfrac5{13}-\arccos\dfrac35$$ answered Aug 10, 2017 at 1056 $\endgroup$ You must log in to answer this question. Not the answer you're looking for? Browse other questions tagged . / Fórmulas / Matemática / 1. Relações trigonométricas fundamentais $\mathrm{sen}^{2} a + \cos^{2} a = 1$ $tg a = \frac{sen a}{\cos a}$ $cotg a = \frac{\cos a }{sen a}$ $sec a = \frac{1}{\cos a}$ $cossec a = \frac{1}{sen a}$ 2. Relações trigonométricas derivadas $tg^{2} a + 1 = sec^{2} a$ $cotg^{2} a +1 = cossec^{2} a$ 3. Seno da soma - Cosseno da soma - Tangente da soma $sena+b = sena \ . \cos b + senb \ . \cosa$ $\cos a+b = \cos a \ . \cos b - sena \ . senb$ $tga+b = \frac{tga + tgb}{1-tga \ . tgb}$ 4. Seno da diferença - Cosseno da diferença - Tangente da diferença $sena-b = sena \ . \cos b - senb \ . \cos a$ $\cos a-b = \cos a \ . \cos b + sena \ . senb$ $tga-b = \frac{tga - tgb}{1+tga \ . tgb}$ 5. Soma de senos - Soma de cossenos - Soma de tangentes $sen a + sen b = 2 sen \left \frac{a+b}{2} \right \ . \cos \left \frac{a-b}{2} \right$ $ \cos a+ \cos b = 2 \cos \left\frac{a+b}{2} \right \ . \cos \left\frac{a-b}{2}\right$ $tg a + tg b = \left \frac{sen a+b}{\cos a \ . \cos b} \right$ 6. Subtração de senos - Subtração de cossenos - Subtração de tangentes $ sen a - sen b = 2 sen \left \frac{a-b}{2} \right \ . \cos \left \frac{a+b}{2} \right $ $ \cos a - \cos b = -2 sen \left \frac{a+b}{2} \right \ . sen \left \frac{a-b}{2} \right$ $tg a -tg b = \left \frac{sen a-b}{\cos a \ . \cos b} \right $ 7. Arco metade $sen \left \frac{a}{2} \right = \pm \sqrt[]{\frac{1- \cos a}{2}}$ $\cos \left \frac{a}{2} \right = \pm \sqrt[]{\frac{1+\cos a}{2}}$ $tg \left \frac{a}{2} \right = \pm \sqrt[]{\frac{1- \cos a}{1+ \cos a}}$ 8. Arco duplo $sen2a = 2sena \ . \cos a$ $\cos 2a = \cos^{2} a - sen^{2}a$ $tg2a = \frac{2tga}{1-tg^{\style{font-familyArial; font-size31px;}{2}}a}$ 9. Arco triplo $sen3a = 3sena-4sen^{3}a$ $\cos 3a = 4 \cos^{3} 3a - 3 \cos a$ $tg 3a = \frac{3tg a-tg^{3}a}{1-3tg^{\style{font-familyArial; font-size30px;}2}a}$ 10. Arco quádruplo $sen4a =4sena \ . \cos a -8sen^{3} a \ . \cos a $ $\cos 4a = 8 \cos^{4} a - 8 \cos^{2} a +1$ $tg 4a = \frac{4tg a- 4tg^{3}a}{1-6tg^{\style{font-familyArial; font-size30px;}2}a+tg^{\style{font-familyArial; font-size30px;}4} a}$ 11. Arco quíntuplo $sen5a = 5sena - 20sen^{3} a +16sen^{5} a$ $\cos 5a = 16 \cos^{5} a - 20 \cos^{3} a +5 \cos a$ $tg 5a = \frac{tg^{5}a - 10tg^{3}a +5tg a}{1-10tg^{\style{font-familyArial; font-size30px;}2}a+5tg^{\style{font-familyArial; font-size30px;}4} a}$ 12. Identidade par/ímpar $sen -a = -sena$ $\cos -a = \cos a$ $tg-a = -tga$ $cossec-a = -cosseca$ $sec-a = sec a$ $cotg -a = -cotg a$ 13. Arcos complementares $sen 90° \hspace{ -a = \cos a$ $\cos 90° \hspace{ -a = sen a$ $tg 90° \hspace{ -a = cotg a$ $cotg 90° \hspace{ -a = tg a$ $sec 90° \hspace{ -a = cossec a$ $cossec 90° \hspace{ -a = sec a$ 14. Periodicidade $sen 360° \hspace{ +a = sen a$ $\cos 360° \hspace{ +a = \cos a$ $tg 180° \hspace{ +a = tga$ $cotg 180° \hspace{ +a = cotga$ $sec 360° \hspace{ +a = seca$ $cossec 360° \hspace{ +a = cosseca$ 15. Transformação de produto para soma $sen a \ . sen b = \frac { \cos a-b - \cosa+b}{2}$ $\cos a \ . \cos b = \frac {\cos a-b + \cos a+b}{2}$ $sen a \ . \cos b = \frac {sen a-b+sen a+b}{2}$ $tg a \ . tgb = \frac {tg a + tgb}{cotga + cotgb}$ $cotga \ . cotgb = \frac {cotga + cotgb}{tg a + tg b}$ $tga \ . cotgb = \frac {tg a + cotg b}{cotg a + tg b}$ 16. Potências de seno e cosseno $sen^{2} a = \frac{1-cos 2a}{2}$ $sen^{3} a = \frac{3sen a -sen3a}{4}$ $sen^{4} a = \frac{\cos 4a -4 \cos 2a + 3}{8}$ $sen^{5} a = \frac{10sen a -5 sen 3a + sen5a}{16}$ $sen^{6} a = \frac{10 - 15 \cos 2a +6 \cos 4a -cos 6a}{32}$ $\cos^{2} a = \frac{1+ \cos 2a}{2}$ $\cos^{3} a = \frac{3 \cos a +cos3a}{4}$ $\cos^{4} a = \frac{\cos 4a +4 \cos 2a + 3}{8}$ $\cos^{5} a = \frac{10 \cos a +5 sen 3a + \cos 5a}{16}$ $\cos^{6} a = \frac{10 + 15 \cos 2a +6 \cos 4a + cos 6a}{32}$  If \[\sin A = \frac{4}{5}\] and \[\cos B = \frac{5}{13}\], where 0 < A, \[B < \frac{\pi}{2}\], find the value of the following sin A + B Given \[ \sin A = \frac{4}{5}\text{ and }\cos B = \frac{5}{13}\]We know that\[ \cos A = \sqrt{1 - \sin^2 A}\text{ and }\sin B = \sqrt{1 - \cos^2 B} ,\text{ where }0 < A , B < \frac{\pi}{2}\]\[ \Rightarrow \cos A = \sqrt{1 - \left \frac{4}{5} \right^2} \text{ and }\sin B = \sqrt{1 - \left \frac{5}{13} \right^2}\]\[ \Rightarrow \cos A = \sqrt{1 - \frac{16}{25}}\text{ and }\sin B = \sqrt{1 - \frac{25}{169}}\]\[ \Rightarrow \cos A = \sqrt{\frac{9}{25}}\text{ and }\sin B = \sqrt{\frac{144}{169}}\]\[ \Rightarrow \cos A = \frac{3}{5}\text{ and }\sin B = \frac{12}{13}\]Now,\[ \sin\left A + B \right = \sin A \cos B + \cos A \sin B\]\[ = \frac{4}{5} \times \frac{5}{13} + \frac{3}{5} \times \frac{12}{13}\]\[ = \frac{20}{65} + \frac{36}{65}\]\[ = \frac{56}{65}\] Here, colorgreenI^st Quadrant=> 0 all+ve sina=5/13=>cosa=sqrt1-sin^2a=sqrt1-25/169=12/13 cosb=4/5=>sinb=sqrt1-cos^2b=sqrt1-16/25=3/5 colorredisina+b=sinacosb+cosasinb colorwhiteisina+b=5/13xx4/5+12/13xx3/5=20/65+36/65=56/65 colorblueiicosa-b=cosacosb+sinasinb colorwhiteiicosa-b=12/13xx4/5+5/13xx3/5=48/65+15/65=63/65 colorvioletiiicosb/2=sqrt1+cosb/2=sqrt1+4/5/2=sqrt9/10=3/sqrt10 colororangeivsin2a=2sinacosa=2xx5/13xx12/13=120/169

sin a 4 5 cos b 5 13