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Access these online resources for additional instruction and practice with sine and cosine functions.
Cosine | $\mathrm{cos}\text{\hspace{0.17em}}t=x$ |
Sine | $\mathrm{sin}\text{\hspace{0.17em}}t=y$ |
Pythagorean Identity | ${\mathrm{cos}}^{2}t+{\mathrm{sin}}^{2}t=1$ |
Describe the unit circle.
The unit circle is a circle of radius 1 centered at the origin.
What do the x- and y- coordinates of the points on the unit circle represent?
Discuss the difference between a coterminal angle and a reference angle.
Coterminal angles are angles that share the same terminal side. A reference angle is the size of the smallest acute angle, $\text{\hspace{0.17em}}t,$ formed by the terminal side of the angle $\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ and the horizontal axis.
Explain how the cosine of an angle in the second quadrant differs from the cosine of its reference angle in the unit circle.
Explain how the sine of an angle in the second quadrant differs from the sine of its reference angle in the unit circle.
The sine values are equal.
For the following exercises, use the given sign of the sine and cosine functions to find the quadrant in which the terminal point determined by $\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ lies.
$\text{sin}(t)<0\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\text{cos}(t)<0$
$\text{sin}(t)>0\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\mathrm{cos}(t)>0$
I
$\text{sin}(t)>0\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\mathrm{cos}(t)<0$
$\text{sin}(t)>0\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\mathrm{cos}(t)>0$
IV
For the following exercises, find the exact value of each trigonometric function.
$\mathrm{sin}\text{\hspace{0.17em}}\frac{\pi}{2}$
$\mathrm{sin}\text{\hspace{0.17em}}\frac{\pi}{3}$
$\frac{\sqrt{3}}{2}$
$\mathrm{cos}\text{\hspace{0.17em}}\frac{\pi}{2}$
$\mathrm{cos}\text{\hspace{0.17em}}\frac{\pi}{3}$
$\frac{1}{2}$
$\mathrm{sin}\text{\hspace{0.17em}}\frac{\pi}{4}$
$\mathrm{cos}\text{\hspace{0.17em}}\frac{\pi}{4}$
$\frac{\sqrt{2}}{2}$
$\mathrm{sin}\text{\hspace{0.17em}}\frac{\pi}{6}$
$\mathrm{sin}\text{\hspace{0.17em}}\frac{3\pi}{2}$
$\mathrm{cos}\text{\hspace{0.17em}}0$
$\mathrm{cos}\text{\hspace{0.17em}}\frac{\pi}{6}$
$\frac{\sqrt{3}}{2}$
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