삼각함수의 뜻과 관계

For the following exercises, use the angle in the unit circle to find the value of the each of the six trigonometric functions.

For the following exercises, use the angle in the unit circle to find the value of the each of the six trigonometric functions.

For the following exercises, use the angle in the unit circle to find the value of the each of the six trigonometric functions.

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 $f(x)=\sec \,x?$

For the following exercises, simplify the expression, and then graph both expressions as functions to verify the graphs are identical. Confirm your answer using a graphing calculator.

$\cos \left(\frac{\pi }{2}-x\right)$

For the following exercises, simplify the expression, and then graph both expressions as functions to verify the graphs are identical. Confirm your answer using a graphing calculator.

$\sin (\pi -x)$

For the following exercises, simplify the expression, and then graph both expressions as functions to verify the graphs are identical. Confirm your answer using a graphing calculator.

$\tan \left(\frac{\pi }{3}+x\right)$

For the following exercises, simplify the expression, and then graph both expressions as functions to verify the graphs are identical. Confirm your answer using a graphing calculator.

$\sin \left(\frac{\pi }{3}+x\right)$

For the following exercises, simplify the expression, and then graph both expressions as functions to verify the graphs are identical. Confirm your answer using a graphing calculator.

$\tan \left(\frac{\pi }{4}-x\right)$

For the following exercises, simplify the expression, and then graph both expressions as functions to verify the graphs are identical. Confirm your answer using a graphing calculator.

$\cos \left(\frac{7\pi }{6}+x\right)$

For the following exercises, simplify the expression, and then graph both expressions as functions to verify the graphs are identical. Confirm your answer using a graphing calculator.

$\sin \left(\frac{\pi }{4}+x\right)$

For the following exercises, simplify the expression, and then graph both expressions as functions to verify the graphs are identical. Confirm your answer using a graphing calculator.

$\cos \left(\frac{5\pi }{4}+x\right)$

For the following exercises, use a graph to determine whether the functions are the same or different. If they are the same, show why. If they are different, replace the second function with one that is identical to the first. (Hint: think $2x=x+x.$ )

$f(x)=\sin (4x)-\sin (3x)\cos \,x,g(x)=\sin \,x\,\cos (3x)$

For the following exercises, use a graph to determine whether the functions are the same or different. If they are the same, show why. If they are different, replace the second function with one that is identical to the first. (Hint: think $2x=x+x.$ )

$f(x)=\cos (4x)+\sin \,x\,\sin (3x),g(x)=-\cos \,x\,\cos (3x)$

For the following exercises, use a graph to determine whether the functions are the same or different. If they are the same, show why. If they are different, replace the second function with one that is identical to the first. (Hint: think $2x=x+x.$ )

$f(x)=\sin (3x)\cos (6x),g(x)=-\sin (3x)\cos (6x)$

For the following exercises, use a graph to determine whether the functions are the same or different. If they are the same, show why. If they are different, replace the second function with one that is identical to the first. (Hint: think $2x=x+x.$ )

$f(x)=\sin (4x),g(x)=\sin (5x)\cos \,x-\cos (5x)\sin \,x$

For the following exercises, use a graph to determine whether the functions are the same or different. If they are the same, show why. If they are different, replace the second function with one that is identical to the first. (Hint: think $2x=x+x.$ )

$f(x)=\sin (2x),g(x)=2\,\sin \,x\,\cos \,x$

For the following exercises, use a graph to determine whether the functions are the same or different. If they are the same, show why. If they are different, replace the second function with one that is identical to the first. (Hint: think $2x=x+x.$ )

$f(\theta )=\cos (2\theta ),g(\theta )={\cos }^{2}\theta -{\sin }^{2}\theta$

For the following exercises, use a graph to determine whether the functions are the same or different. If they are the same, show why. If they are different, replace the second function with one that is identical to the first. (Hint: think $2x=x+x.$ )

$f(\theta )=\tan (2\theta ),g(\theta )=\frac{\tan \,\theta }{1+{\tan }^{2}\theta }$

For the following exercises, use a graph to determine whether the functions are the same or different. If they are the same, show why. If they are different, replace the second function with one that is identical to the first. (Hint: think $2x=x+x.$ )

$f(x)=\sin (3x)\sin \,x,g(x)={\sin }^{2}(2x){\cos }^{2}x-{\cos }^{2}(2x){\sin }^{2}x$