91Ó°ÊÓ

Four functions \(S, C, T,\) and \(D\) are defined as follows: \(\left.\begin{array}{l}S(\theta)=\sin \theta \\ C(\theta)=\cos \theta \\\ T(\theta)=\tan \theta \\ D(\theta)=2 \theta\end{array}\right\\} \quad 0^{\circ}<\theta<90^{\circ}\) In each case, use the values to decide if the statement is true or false. A calculator is not required. $$2\left[S\left(30^{\circ}\right)\right]=s\left(60^{\circ}\right)$$

Are there any real numbers \(x\) with the property that \(x\) degrees equals \(2 x\) radians? If so, find them; if not, explain why not.

Four functions \(S, C, T,\) and \(D\) are defined as follows: \(\left.\begin{array}{l}S(\theta)=\sin \theta \\ C(\theta)=\cos \theta \\\ T(\theta)=\tan \theta \\ D(\theta)=2 \theta\end{array}\right\\} \quad 0^{\circ}<\theta<90^{\circ}\) In each case, use the values to decide if the statement is true or false. A calculator is not required. $$T\left(45^{\circ}\right)-(C \circ D)\left(30^{\circ}\right)>0$$

Use the given information to determine the remaining five trigonometric values. $$\sin \theta=-24 / 25, \quad 180^{\circ}<\theta<270^{\circ}$$

Four functions \(S, C, T,\) and \(D\) are defined as follows: \(\left.\begin{array}{l}S(\theta)=\sin \theta \\ C(\theta)=\cos \theta \\\ T(\theta)=\tan \theta \\ D(\theta)=2 \theta\end{array}\right\\} \quad 0^{\circ}<\theta<90^{\circ}\) In each case, use the values to decide if the statement is true or false. A calculator is not required. $$(T \circ D)\left(30^{\circ}\right)>1$$

Use the given information to determine the remaining five trigonometric values. $$\cos \theta=-3 / 5, \quad 180^{\circ}<\theta<270^{\circ}$$

Use the given information to determine the remaining five trigonometric values. $$\cos \theta=1 / 4, \quad 270^{\circ}<\theta<360^{\circ}$$

Four functions \(S, C, T,\) and \(D\) are defined as follows: \(\left.\begin{array}{l}S(\theta)=\sin \theta \\ C(\theta)=\cos \theta \\\ T(\theta)=\tan \theta \\ D(\theta)=2 \theta\end{array}\right\\} \quad 0^{\circ}<\theta<90^{\circ}\) In each case, use the values to decide if the statement is true or false. A calculator is not required. $$T\left(60^{\circ}\right)=2\left[T\left(30^{\circ}\right)\right]$$

Four functions \(S, C, T,\) and \(D\) are defined as follows: \(\left.\begin{array}{l}S(\theta)=\sin \theta \\ C(\theta)=\cos \theta \\\ T(\theta)=\tan \theta \\ D(\theta)=2 \theta\end{array}\right\\} \quad 0^{\circ}<\theta<90^{\circ}\) In each case, use the values to decide if the statement is true or false. A calculator is not required. $$S\left(45^{\circ}\right)-C\left(45^{\circ}\right)=0$$

Use the given information to determine the remaining five trigonometric values. $$\sec \beta=3, \quad 0^{\circ}<\beta<90^{\circ}$$