Chapter 6

Carry out the indicated operations. (a) \(-S C+12 S C\) (b) \(-\sin \theta \cos \theta+12 \sin \theta \cos \theta\)

Sketch each angle in standard position and specify the reference angle or reference number. (a) \(110^{\circ}\) (b) \(240^{\circ}\) (c) \(60^{\circ}\) (d) \(-60^{\circ}\)

Sketch each angle in standard position. (a) \(\pi / 4\) (b) \(-\pi / 4\) (c) \(3 \pi / 4\)

Carry out the indicated operations. (a) \(10 S C+4 S C-16 S C\) (b) \(10 \sin \theta \cos \theta+4 \sin \theta \cos \theta-16 \sin \theta \cos \theta\)

Sketch each angle in standard position and specify the reference angle or reference number. (a) \(300^{\circ} \quad\) (b) \(1000^{\circ}\) (c) \(-15^{\circ}\) (d) \(15^{\circ}\)

Sketch each angle in standard position. (a) \(\pi / 6\) (b) \(-\pi / 6\) (c) \(-5 \pi / 6\)

Carry out the indicated operations. (a) \(4 C^{3} S-12 C^{3} S\) (b) \(4 \cos ^{3} \theta \sin \theta-12 \cos ^{3} \theta \sin \theta\)

Sketch each angle in standard position and specify the reference angle or reference number. (a) \(3 \pi / 4 (b) \)-5 \pi / 6\( (c) \)5 \pi / 3\( (d) \)7 \pi / 6$

Sketch each angle in standard position. (a) \(\pi / 3\) (b) \(-5 \pi / 3\) (c) \(-7 \pi / 3\)

Carry out the indicated operations. (a) \(-C^{2} S^{2}+(2 S C)^{2}\) (b) \(-\cos ^{2} \theta \sin ^{2} \theta+(2 \sin \theta \cos \theta)^{2}\)

Sketch each angle in standard position and specify the reference angle or reference number. (a) \(5 \pi / 6\) (b) \(-\pi / 3\) (c) \(2 \pi / 3\) (d) \(5 \pi / 4\)

Sketch each angle in standard position. (a) \(3 \pi / 2\) (b) \(-3 \pi / 2\) (c) \(-5 \pi / 2\)

Carry out the indicated operations. (a) \((1+T)^{2}\) (b) \((1+\tan \theta)^{2}\)

Match an appropriate value from the righthand column with each expression in the left-hand column. (A) \(\sqrt{3} / 2\) (B) \(1 / 2\) (C) \(\sqrt{3} / 3\) (D) \(\sqrt{3}\) (E) \(\sqrt{2}\) (F) \(\sqrt{2} / 2\) (A) \(\sqrt{3}\) (B) \(\sqrt{2}\) (C) \(2 / \sqrt{3}\) (D) \(\sqrt{2} / 2\) (E) 2 (F) \(1 / 2\) (a) \(\cos (\pi / 3)\) (b) \(\sin (\pi / 3)\) (c) \(\tan (\pi / 3)\) (d) \(\cos (\pi / 6)\) (e) \(\sin (\pi / 6)\) (f) \(\tan (\pi / 6)\)

Suppose that \(\triangle A B C\) is a right triangle with \(\angle C=90^{\circ}\) If \(A C=3\) and \(B C=2,\) find the following quantities. (a) \(\cos A, \sin A, \tan A\) (b) \(\sec B, \csc B, \cot B\)

Sketch each angle in standard position. (a) \(210^{\circ}\) (b) \(-210^{\circ}\) (c) \(-570^{\circ}\)

Convert to radian measure. Express your answers both in terms of \(\pi\)and as decimal approximations rounded to two decimal places. (a) \(45^{\circ}\) (b) \(90^{\circ}\) (c) \(135^{\circ}\)

Carry out the indicated operations. (a) \((3-2 T)^{2}\) (b) \((3-2 \tan \theta)^{2}\)

Suppose that \(\triangle A B C\) is a right triangle with \(\angle C=90^{\circ}\) If \(A C=6\) and \(B C=2,\) find the following quantities. (a) \(\cos A, \sin A, \tan A\) (b) \(\sec B, \csc B, \cot B\)

Sketch each angle in standard position. (a) \(45^{\circ}\) (b) \(-225^{\circ}\) (c) \(315^{\circ}\)

Convert to radian measure. Express your answers both in terms of \(\pi\)and as decimal approximations rounded to two decimal places. (a) \(30^{\circ}\) (b) \(150^{\circ}\) (c) \(300^{\circ}\)

Carry out the indicated operations. (a) \((T+3)(T-2)\) (b) \((\tan \theta+3)(\tan \theta-2)\)

Suppose that \(\triangle A B C\) is a right triangle with \(\angle C=90^{\circ}\) If \(A B=13\) and \(B C=5,\) compute the values of the six trigonometric functions of angle \(B\)

Sketch each angle in standard position. (a) \(120^{\circ}\) (b) \(-120^{\circ}\) (c) \(300^{\circ}\)

Convert to radian measure. Express your answers both in terms of \(\pi\)and as decimal approximations rounded to two decimal places. (a) \(0^{\circ}\) (b) \(360^{\circ}\) (c) \(450^{\circ}\)

Carry out the indicated operations. (a) \(\left(S^{2}-3\right)\left(S^{2}+3\right)\) (b) \(\left(\sec ^{2} \theta-3\right)\left(\sec ^{2} \theta+3\right)\)

Suppose that \(\triangle A B C\) is a right triangle with \(\angle C=90^{\circ}\) If \(A B=3\) and \(A C=1,\) compute the values of the six trigonometric functions of angle \(A\)

Sketch each angle in standard position. (a) \(450^{\circ}\) (b) \(-180^{\circ}\) (c) \(270^{\circ}\)

Convert to radian measure. Express your answers both in terms of \(\pi\)and as decimal approximations rounded to two decimal places. (a) \(36^{\circ}\) (b) \(35^{\circ}\) (c) \(720^{\circ}\)

Carry out the indicated operations. (a) \(\frac{S-C}{C-S}\) (b) \(\frac{\sin \theta-\cos \theta}{\cos \theta-\sin \theta}\)

Suppose that \(\triangle A B C\) is a right triangle with \(\angle C=90^{\circ}\) If \(A B=3\) and \(A C=1,\) compute the values of the six trigonometric functions of angle \(A\) If \(A C=1\) and \(B C=3 / 4,\) compute each quantity. (a) \(\sin B, \cos A\) (b) \(\sin A, \cos B\) (c) \((\tan A)(\tan B)\)

Use the definitions (not a calculator) to evaluate the six trigonometric functions of each angle. If a value is undefined, state this. $$\pi$$

Convert the radian measures to degrees. (a) \(\pi / 12\) (b) \(\pi / 6\) (c) \(\pi / 4\)

Carry out the indicated operations. (a) \(\frac{5-2 T}{2 T-5}\) (b) \(\frac{5-2 \tan \theta}{2 \tan \theta-5}\)

Use the definitions (not a calculator) to evaluate the six trigonometric functions of each angle. If a value is undefined, state this. $$-\pi / 2$$

Convert the radian measures to degrees. (a) \(3 \pi\) (b) \(3 \pi / 2\) (c) \(2 \pi\)

Carry out the indicated operations. (a) \(C+\frac{2}{S}\) (b) \(\cos A+\frac{2}{\sin A}\)

Suppose that \(\triangle A B C\) is a right triangle with \(\angle C=90^{\circ}\) If \(A B=3\) and \(A C=1,\) compute the values of the six trigonometric functions of angle \(A\) If \(A B=25\) and \(A C=24,\) compute each of the required quantities. (a) \(\cos A, \sin A, \tan A\) (b) \(\cos B, \sin B, \tan B\) (c) \((\tan A)(\tan B)\)

Use the definitions (not a calculator) to evaluate the six trigonometric functions of each angle. If a value is undefined, state this. $$-2 \pi$$

Convert the radian measures to degrees. (a) \(\pi / 3\) (b) \(5 \pi / 3\) (c) \(4 \pi\)

Carry out the indicated operations. (a) \(\frac{1}{S}-\frac{3}{C}\) (b) \(\frac{1}{\sin A}-\frac{3}{\cos A}\)

Suppose that \(\triangle A B C\) is a right triangle with \(\angle C=90^{\circ}\) If \(A B=3\) and \(A C=1,\) compute the values of the six trigonometric functions of angle \(A\) If \(A B=1\) and \(B C=\sqrt{3} / 2,\) compute the following. (a) \(\cos A, \sin B\) (b) \(\tan A, \cot B\) (c) \(\sec A, \csc B\)

Use the definitions (not a calculator) to evaluate the six trigonometric functions of each angle. If a value is undefined, state this. $$3 \pi / 2$$

Convert the radian measures to degrees. (a) \(5 \pi / 6\) (b) \(11 \pi / 6\) (c) 0

Factor each expression. (a) \(T^{2}+8 T-9\) (b) \(\tan ^{2} \beta+8 \tan \beta-9\)

Verify that each equation is correct by evaluating each side. Do not use a calculator. $$\cos 60^{\circ}=\cos ^{2} 30^{\circ}-\sin ^{2} 30^{\circ}$$

Use the definitions (not a calculator) to evaluate the six trigonometric functions of each angle. If a value is undefined, state this. $$-3 \pi / 2$$

Convert the radian measures to degrees. Bound the answers to two decimal places. $$\begin{array}{lll} \text { (a) } 2 & \text { (b) } 3 & \text { (c) } \pi^{2} \end{array}$$

Factor each expression. (a) \(3 S^{2}+2 S-8\) (b) \(3 \sec ^{2} \beta+2 \sec \beta-8\)

Verify that each equation is correct by evaluating each side. Do not use a calculator. $$\cos 60^{\circ}=1-2 \sin ^{2} 30^{\circ}$$