Do \(\pi< a< \frac{3\pi}{2}\Rightarrow cosa< 0\)
\(cosa=-\sqrt{1-sin^2a}=-\sqrt{1-0,6^2}=-\frac{4}{5}\)
\(tana=\frac{sina}{cosa}=-\frac{3}{4}\)
\(cota=\frac{1}{tana}=-\frac{4}{3}\)
Rút gọn biểu thức
\(E = cot(5π+α).cos(α-\dfrac{3π}{2})+cos(α-2π)-2.cos(\dfrac{π}{2}+α)\)\(D = sin(π+α)-cos(\dfrac{π}{2}-α)+cot(4π-α)+tan(\dfrac{5π}{2}-α)\)
Tính cos(α-π/3) biết sinα=3/5 và π/2
Biết rằng \(sin\left(x-\frac{\pi}{3}\right)+sin\frac{13\pi}{2}=sin\left(x+\frac{\pi}{3}\right)\). Tính gtri của \(cosx\)
cho sin α =\(\frac{-5}{13}\) và \(\frac{3\pi}{2}\) < α < π . Tìm sin α , tan α , cot α
Rút gọn các biểu thức sau :
a) A= 3sin(11\(\pi\) -x) sin(\(\frac{5\pi}{2}-x\)) +2sin(9\(\pi\)+x)
b) B=sin(1980\(^o\)+x)-cos(90\(^o\) -x)+tan(\(270^o-x\)) +cot (360\(^o\) -x)
c) C=-2sin(\(\frac{-5\pi}{2}\)+x)-3cos(3\(\pi\)-x)+5sin(\(\frac{7\pi}{2}\)-x)+cot(\(\frac{3\pi}{2}\)-x)
d) D=tan(x-\(\pi\)) cos (x-\(\frac{\pi}{2}\))cos(x+\(\pi\))
e) E=cos(\(\frac{115\pi}{2}-x\))+sin(\(x-\frac{235\pi}{2}\))+cos(x-\(\frac{187\pi}{2}\))+sin(\(\frac{143\pi}{2}-x\))
f) F= cot(x-\(107\pi\)) cos(x-\(\frac{303\pi}{2}\))+cos(x+1008\(\pi\))-3sin(x-1019\(\pi\))
g) G=cot(19\(\pi\)-x)+cos(x-37\(\pi\))+sin(\(-\frac{31\pi}{2}-x\))+tan(x-\(\frac{47\pi}{2}\))
h) H=cos(1170\(^o\)+x)+2sin(x-540\(^o\))-tan(630\(^o\)+x) cot(810\(^o\)-x)
i) I=\(\frac{sin\left(\pi-x\right)cos\left(x-\frac{9\pi}{2}\right)tan\left(9\pi+x\right)}{cos\left(7\pi-x\right)sin\left(\frac{7\pi}{2}-x\right)cot\left(x-\frac{17\pi}{2}\right)}\)
Cho \(tan\alpha=3\), \(\alpha\in\left(\pi;\frac{3\pi}{2}\right)\)
Tính \(tan\frac{\alpha}{2}\), \(tan4\alpha\), \(sin\left(\frac{\alpha}{2}+\frac{\pi}{4}\right)\)
cho sin\(\alpha=\frac{3}{4}\) , \(\frac{\pi}{2}< \alpha< \pi\)
tinh A= \(\frac{2tan\alpha-3cot\alpha}{cos\alpha-tan\alpha}\)
cho \(sin\alpha+cos\alpha=\frac{1}{2}\) với \(\frac{3\pi}{4}< \alpha< \pi\). tính \(tan2\alpha\)
Cho \(sin\alpha=\frac{-2}{3}\); \(\alpha\in\) góc phần tư thứ (III).
a) Tính \(cos\alpha\), \(tan\left(\alpha+\pi\right)\)
b) Tính \(sin\left(\alpha+\frac{3\pi}{2}\right)\)
