삼각함수 전체 문제

Draw the angle $-\frac{\pi }{6}$ in standard position on the Cartesian plane.

A carnival has a Ferris wheel with a diameter of 80 feet. The time for the Ferris wheel to make one revolution is 75 seconds. What is the linear speed in feet per second of a point on the Ferris wheel? What is the angular speed in radians per second?

Find the missing sides of the triangle $ABC:\sin \,B=\frac{3}{4},c=12.$

Find the missing sides of the triangle.

The angle of elevation to the top of a building in Chicago is found to be 9 degrees from the ground at a distance of 2000 feet from the base of the building. Using this information, find the height of the building.

Find the exact value of $\sin \,\frac{\pi }{6}.$

Compute sine of $240^\circ .$

State the domain of the sine and cosine functions.

State the range of the sine and cosine functions.

Find the exact value of $\cot \,\frac{\pi }{4}.$

Find the exact value of $\tan \,\frac{\pi }{3}.$

Use reference angles to evaluate $\csc \,\frac{7\pi }{4}.$

Use reference angles to evaluate $\tan \,210^\circ .$

If $\csc \,t=0.68,$ what is the $\csc (-t)?$

If $\cos \,t=\frac{\sqrt{3}}{2},$ find $\cos (t-2\pi ).$

Find the missing angle: $\cos \left(\frac{\pi }{6}\right)=\sin (\_\_\_)$

Why are the sine and cosine functions called periodic functions?

How does the graph of $y=\sin \,x$ compare with the graph of $y=\cos \,x?$ Explain how you could horizontally translate the graph of $y=\sin \,x$ to obtain $y=\cos \,x.$

For the equation $A\,\cos (Bx+C)+D,$ what constants affect the range of the function and how do they affect the range?

How does the range of a translated sine function relate to the equation $y=A\,\sin (Bx+C)+D?$