Tính các giá trị lượng giác của góc\(\alpha\), nếu :
a) \(\cos\alpha=\dfrac{4}{13}\) và \(0< \alpha< \dfrac{\pi}{2}\)
b) \(\sin\alpha=-0,7\) và \(\pi< \alpha< \dfrac{3\pi}{2}\)
c) \(\tan\alpha=-\dfrac{15}{7}\) và \(\dfrac{\pi}{2}< \alpha< \pi\)
d) \(\cot\alpha=-3\) và \(\dfrac{3\pi}{2}< \alpha< 2\pi\)
a) Do 0 < α <
nên sinα > 0, tanα > 0, cotα > 0
sinα =![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20%5Csqrt%7B1-%28%5Cfrac%7B4%7D%7B13%7D%29%5E%7B2%7D%7D%3D%5Cfrac%7B%5Csqrt%7B153%7D%7D%7B13%7D%3D%5Cfrac%7B3%5Csqrt%7B17%7D%7D%7B13%7D)
cotα =
; tanα = ![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20%5Cfrac%7B3%5Csqrt%7B17%7D%7D%7B4%7D)
b) π < α <
nên sinα < 0, cosα < 0, tanα > 0, cotα > 0
cosα = -√(1 - sin2 α) = -√(1 - 0,49) = -√0,51 ≈ -0,7141
tanα ≈ 0,9802; cotα ≈ 1,0202.
c)
< α < π nên sinα > 0, cosα < 0, tanα < 0, cotα < 0
cosα =
≈ -0,4229.
sinα =![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20%5Csqrt%7B%5Cfrac%7B1%7D%7B1+cot%5E%7B2%7D%5Calpha%20%7D%7D%3D%5Csqrt%7B%5Cfrac%7B1%7D%7B1+%28%5Cfrac%7B7%7D%7B15%7D%29%5E%7B2%7D%7D%7D%3D%5Cfrac%7B15%7D%7B%5Csqrt%7B274%7D%7D%3D0%2C9062)
cotα = -![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20%5Cfrac%7B7%7D%7B15%7D)
d) Vì
< α < 2π nên sinα < 0, cosα > 0, tanα < 0, cotα < 0
Ta có: tanα =![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20%5Cfrac%7B1%7D%7Bcot%5Calpha%20%7D%3D-%5Cfrac%7B1%7D%7B3%7D)
sinα =cosα =![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cdpi%7B80%7D%20%5Csqrt%7B%5Cfrac%7B1%7D%7B1+tan%5E%7B2%7D%5Calpha%20%7D%7D%3D%5Csqrt%7B%5Cfrac%7B1%7D%7B1+%28%5Cfrac%7B1%7D%7B3%7D%5E%7B2%7D%29%7D%7D%3D%5Cfrac%7B3%7D%7B%5Csqrt%7B10%7D%7D%3D0%2C9487)