Name: Class: Date: Use the definitions to evaluate the six trigonometric functions of. In cases in which a radical occurs in a denominator, rationalize the denominator. Suppose that ABC is a right triangle with C = 90. If AC = and BC = 4, find the following quantities. cos A, sin A, tan A cos A = 4 4, sin A = 4, tan A = 4 4 4 cos A = 4 4, sin A = 4 4, tan A = 4 cos A = 4 4, sin A = 4 4, tan A = cos A = 4 4 cos A =, sin A = 4 4 4, tan A = 4 4 4, sin A = 4 4, tan A = 4 Determine whether the equation is correct by evaluating each sid Do not use a calculator. Note: Notation such as sin stands for ( sin ). sin =, tan =, csc = cos =, cot =, sec = sin = cos =, tan =, csc =, cot =, sec = sin =, tan =, csc = cos =, cot =, sec = sin =, tan =, csc = cos =, cot =, sec = sin =, tan =, csc = cos =, cot =, sec = sin 60 = cos 0 + sin 0 no yes 4 Determine whether the equation is correct by evaluating each sid Do not use a calculator. Note: Notation such as sin stands for ( sin ). cos 60 = cos 0 + no yes Determine whether the equation is correct by evaluating each sid Do not use a calculator. Note: Notation such as sin stands for ( sin ) cos 0 + sin 4 + sin 60 =. yes no 6 Determine whether the equation is correct by evaluating each sid Do not use a calculator. sin 60 cos 0 cos 60 sin 0 = yes no PAGE
Name: Class: Date: Carry out the indicated operation. sin cot cot sin 0 Use the given information to determine the value of remaining five trigonometric functions. (Assume that the angle is acut) If a radical appears in the denominator, rationalize the denominator. cot sin tan 8 Factor the expression. tan + 4 tan (tan )(tan + ) (tan )(tan + ) (tan )(tan + ) (tan 4)(tan + ) (tan 6)(tan + 4) 9 Factor the expression. sec + 0 sec 8 ( sec )(sec + ) ( sec )(sec + ) ( sec )(sec + ) ( sec )(sec + ) ( sec )(sec + 4) sin = cos = sec =, tan =, cot =, csc = cos =, tan =, cot = sec =, csc = cos =, tan =, cot = sec =, csc = cos =, tan =, cot = sec =, csc = cos =, tan =,,,,, cot =, sec =, csc = PAGE
Name: Class: Date: Use the given information to determine the value of remaining five trigonometric functions. (Assume that the angle is acut) If a radical appears in the denominator, rationalize the denominator. cos B = 4 sin B = 9 4, csc B = 9 sin B = 4, csc B = sin B = 9, tan B = 4, cot B = 4, sec B =, tan B = 4, cot B = 4, sec B =, tan B = 4, cot B = 4, sec B =, csc B = 4 sin B =, csc B = 4 sin B = 4, csc B =, tan B =, cot B = 4, sec B = 4, tan B = 4, cot B = 4, sec B = Rewrite in terms of sine and cosine, and simplify the expression: 4 Rewrite in terms of sine and cosine, and simplify the expression: 4 sin + 8 sin 4 8 sin + sin 4 sin + 8 cos + cos cos + cos + sin + 4 4 sin Rewrite in terms of sine and cosine, and simplify the expression: cot + csc sin cos 0 cos + 6 Refer to the figur If A = 4 and AB = 40 cm, find AC. cos C sin C cos C sin C (Hint: Factor the numerator.) cos(c) sin(c) cos(c) cos(c) + sin(c) sin(c) cos C sin C Rewrite in terms of sine and cosine, and simplify the expression: cos sec cot csc cos sin sec cot AC = 40 cm AC = 0 cm AC = 40 cm AC = cm AC = 0 cm A ladder 4 ft long leans against a building. The ladder forms and angle of 4 with the groun How high up the side of the building does the ladder reach? ft 4 ft 4 ft ft ft PAGE
Name: Class: Date: 8 From a point level with and 000 ft away from the base of a From a point on ground level, you measure the angle of monument, the angle of elevation to the top of the monument is elevation to the top of a mountain to be. Then you walk 9.. Determine the height of the monument to the nearest 60 m farther away from the mountain and find that the angle foot. of elevation is now. Find the height of the mountain. ft. m m m 9 Find the area of the triangl 69 m 4 m In the figure, AB = 6 in. Express x as a function of. area = in. 0 Find the area of the triangl Use a calculator and round your final answer to two decimal places. tan 6 cos sin 6 cot 6 cos cot 6 sin tan cos 6 tan 4 Use the definitions (not a calculator) to evaluate the six trigonometric functio of the angl 80.9 cm.9 cm.8 cm.04 cm.08 cm An observer in a lighthouse is 66 ft above the surface of the water. The observer sees a ship and finds the angle of depression to be 0.. Estimate the distance of the ship from the base of the lighthous ft 8 ft 6 ft 4 ft 60 ft sin 80 = 0 cos 80 = csc 80 is undefined sec 80 = sin 80 is undefined cos 80 = csc 80 = 0 sec 80 = sin 80 = cos 80 = 0 csc 80 = sec 80 is undefined sin 80 = 0 cos 80 = csc 80 is undefined sec 80 = sin 80 = 0 cos 80 = csc 80 = sec 80 is undefined tan 80 = 0 cot 80 is undefined tan 80 = 0 cot 80 is undefined tan 80 is undefined cot 80 = 0 tan 80 is undefined cot 80 = 0 tan 80 = 0 cot 80 is undefined PAGE 4
Name: Class: Date: Use the definitions (not a calculator) to evaluate the six trigonometric functions 6 Use of the definitions of the trigonometric functions to choose the angl correct tabl 990 sin( 990 ) = 0 cos( 990 ) = sin( 990 ) = cos( 990 ) = 0 sin( 990 ) = 0 cos( 990 ) = sin( 990 ) = cos( 990 ) = 0 sin( 990 ) = cos( 990 ) = 0 tan( 990 ) is undefined cot( 990 ) = 0 tan( 990 ) is undefined cot( 990 ) = 0 tan( 990 ) = 0 cot( 990 ) is undefined tan( 990 ) is undefined cot( 990 ) = 0 tan( 990 ) = 0 cot( 990 ) is undefined csc( 990 ) = sec( 990 ) is undefined csc( 990 ) is undefined sec( 990 ) = csc( 990 ) is undefined sec( 990 ) = csc( 990 ) = sec( 990 ) is undefined csc( 990 ) = sec( 990 ) is undefined sin cos tan 0 90 80 0 0 0 40 sin cos tan 0 90 80 0 40 0 0 0 undefined 0 0 0 undefined sin cos tan 0 90 80 0 40 0 undefined undefined 0 0 undefined undefined 0..to be continued PAGE
Name: Class: Date: sin cos tan 0 90 80 0 40 continuation 0 undefined 0 undefined 9 Evaluate the expression using the concept of a reference angl sin( 0 ) 0 Evaluate each expression using the concept of a reference angl cos 6 = sin cos tan 0 90 80 0 40 cos cos( 480 ) 0 undefined 0 undefined Evaluate the expression using the concept of a reference angl 8 Evaluate the expression using the concept of a reference angl 6 6 6 6 cos( 6 ) = sin 6 = sin( 6 ) = Evaluate the expression using the concept of a reference angl cot( 600 ) Evaluate the expression using the concept of a reference angl tan 0 Use the given information to determine the area of the triangl Two of the sides are m and 6 m, and the included angle is 0. PAGE 6