解決cos(99)/cos(33)-sin(99)/sin(33) |Microsoft數學求解器

$$\frac{ \cos ( 99 ) }{ \cos ( 33 ) } - \frac{ \sin ( 99 ) }{ \sin ( 33 ) }$$

評估

$$-\frac{14274147775665639690205403449156}{7137073887832819476834573140475}\approx -2$$

解題步驟

對題中的三角函數求值

$$\frac{-0.15643446504023104}{0.838670567945424} - \frac{0.9876883405951377}{0.5446390350150271}$$

同時對分子與分母乘上 100000000000000000 以展開 \frac{-0.15643446504023104}{0.838670567945424}。

$$\frac{-15643446504023104}{83867056794542400}-\frac{0.9876883405951377}{0.5446390350150271}$$

透過找出與消去 64，對分式 \frac{-15643446504023104}{83867056794542400} 約分至最低項。

$$-\frac{244428851625361}{1310422762414725}-\frac{0.9876883405951377}{0.5446390350150271}$$

同時對分子與分母乘上 10000000000000000 以展開 \frac{0.9876883405951377}{0.5446390350150271}。

$$-\frac{244428851625361}{1310422762414725}-\frac{9876883405951377}{5446390350150271}$$

1310422762414725 和 5446390350150271 的最小公倍數為 7137073887832819476834573140475。將 -\frac{244428851625361}{1310422762414725} 和 \frac{9876883405951377}{5446390350150271} 轉換為分母是 7137073887832819476834573140475 的分數。

$$-\frac{1331254938790678533628944622831}{7137073887832819476834573140475}-\frac{12942892836874961156576458826325}{7137073887832819476834573140475}$$

因為 -\frac{1331254938790678533628944622831}{7137073887832819476834573140475} 和 \frac{12942892836874961156576458826325}{7137073887832819476834573140475} 的分母相同，所以將分子相減即可相減這兩個值。

$$\frac{-1331254938790678533628944622831-12942892836874961156576458826325}{7137073887832819476834573140475}$$

從 -1331254938790678533628944622831 減去 12942892836874961156576458826325 會得到 -14274147775665639690205403449156。

$$-\frac{14274147775665639690205403449156}{7137073887832819476834573140475}$$