삼각함수 전체 문제

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 $\csc \,t=1.68,$ what is the $\csc (-t)?$

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

Which trigonometric functions are even?

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

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.

We know $g(x)=\cos \,x$ is an even function, and $f(x)=\sin \,x$ and $h(x)=\tan \,x$ are odd functions. What about $G(x)={\cos }^{2}x,F(x)={\sin }^{2}x,$ and $H(x)={\tan }^{2}x?$ Are they even, odd, or neither? Why?

Examine the graph of $f(x)=\sec \,x$ on the interval $[-\pi ,\pi ].$ How can we tell whether the function is even or odd by only observing the graph of $f(x)=\sec \,x?$

After examining the reciprocal identity for $\sec \,t,$ explain why the function is undefined at certain points.

All of the Pythagorean Identities are related. Describe how to manipulate the equations to get from ${\sin }^{2}t+{\cos }^{2}t=1$ to the other forms.

For the following exercises, use the fundamental identities to fully simplify the expression.

$\sin \,x\,\cos \,x\,\sec \,x$

For the following exercises, use the fundamental identities to fully simplify the expression.

$\sin (-x)\cos (-x)\csc (-x)$

For the following exercises, use the fundamental identities to fully simplify the expression.

$\tan \,x\sin \,x+\sec \,x{\cos }^{2}x$

For the following exercises, use the fundamental identities to fully simplify the expression.

$\csc \,x+\cos \,x\cot (-x)$

For the following exercises, use the fundamental identities to fully simplify the expression.

$\frac{\cot \,t+\tan \,t}{\sec (-t)}$