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شائع علم المثلثات >

sin(75)-sin(165)

الحلّ

sin (7 5^{\circ}) - sin (16 5^{\circ})

الحلّ

\frac{2}{2}

+1

عشري

0.70710 \dots

خطوات الحلّ

sin (7 5^{\circ}) - sin (16 5^{\circ})

Rewrite using trig identities:

- 2 sin (4 5^{\circ}) cos (12 0^{\circ})

sin (7 5^{\circ}) - sin (16 5^{\circ})

sin (s) - sin (t) = 2 sin (\frac{s - t}{2}) cos (\frac{s + t}{2})

:

Eq u a t i o n 0 :

متطابقة تحويل الجمع لضرب

= 2 sin (\frac{7 5 ^{\circ} - 16 5 ^{\circ}}{2}) cos (\frac{7 5 ^{\circ} + 16 5 ^{\circ}}{2})

بسّط

= 2 sin (- 4 5^{\circ}) cos (12 0^{\circ})

sin (- x) = - sin (x) :

استخدم القانون التالي

sin (- 4 5^{\circ}) = - sin (4 5^{\circ})

= 2 (- sin (4 5^{\circ})) cos (12 0^{\circ})

بسّط

= - 2 sin (4 5^{\circ}) cos (12 0^{\circ})

= - 2 sin (4 5^{\circ}) cos (12 0^{\circ})

استخدم المتطابقة الأساسيّة التالية:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

استخدم المتطابقة الأساسيّة التالية:

cos (12 0^{\circ}) = - \frac{1}{2}

cos (12 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - \frac{1}{2}

= - 2 \cdot \frac{2}{2} (- \frac{1}{2})

- 2 \cdot \frac{2}{2} (- \frac{1}{2})

بسّط:

\frac{2}{2}

- 2 \cdot \frac{2}{2} (- \frac{1}{2})

- (- a) = a

فعّل القانون

= 2 \cdot \frac{2}{2} \cdot \frac{1}{2}

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

:اضرب كسور

= \frac{2 \cdot 1 \cdot 2}{2 \cdot 2}

2 :

إلغ العوامل المشتركة

= \frac{2 \cdot 1}{2}

2 \cdot 1 = 2 :

اضرب

= \frac{2}{2}

= \frac{2}{2}

أمثلة شائعة

arcsin((2sqrt(5))/5)

(sin^3(pi/4))/3