Trigonometry 1st Semester Review Packet (#2) C) 3 D) 2

Transcription

1 Trigonometry 1st Semester Review Packet (#) Name Find the exact value of the trigonometric function. Do not use a calculator. 1) sec A) B) D) ) tan - 5 A) -1 B) - 1 D) - Find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. ) Find sec. A) B) D) 7 8 Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. ) Find cos A) 9 B) 10 9 D) 10 Find the exact value of the indicated trigonometric function of. 5) csc = - 9, in quadrant III Find cot. A) - 9 B) - D) - 9 ) cot = - 5, cos < 0 Find csc. A) B) D)

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3 1) Amplitude of y = - cos 1 x A) B) 8 D) -5 Determine the phase shift of the function. 17) y = - cos (8x + ) A) 8 units to the right B) units to the left units to the right D) 8 units to the left 18) y = - sin 1 x - A) 1 units to the left B) units to the left units to the right D) units to the right Find the exact value of the expression. 19) cos-1 A) B) 11 D) 7 0) sin-1 (- 1 ) A) B) 7 - D) 1) tan-1 A) B) 5 D) ) sin-1 0 A) B) 0 D) - Find all solutions of the equation. ) cos x - 1 = 0 A) x = + n or x = 5 + n B) x = + n or x = 5 + n x = + n or x = 5 + n D) x = + n or x = 5 + n

4 Solve the equation on the interval [0, ). ) cos x + cos x sin x = 0 A) 0,, 7, B), 7,, 11 7, 11 7, D), 11 5) sin x + sin x = 0 A),, 5, 7 B) 0,,, 8, 9 8 D) no solution ) cos x + sin x - = 0 A), B), 5 0,,, 5 D),,, Verify the identity. 7) sin x cos x + cos x sin x =? A) sin x tan x B) 1 + cot x - tan x D) sec x csc x 8) tan x - (1 + tan x) =? A) - sec x B) 1 - sin x 0 D) 1 Find the exact value by using a sum or difference identity. 9) tan 1 1 A) - - B) + - D) - Use a half-angle formula to find the exact value of the expression. 0) sin 8 A) 1 - B) D) Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. 1) B = 15, C = 101, b = A) A =, a = 17.5, c = B) A =, a = 17.5, c = 11.7 A =, a = 11.7, c = 17.5 D) A =, a = 159.7, c = 17.5 ) a = 9, b = 1, c = 15 A) A =, B =, C = 78 B) A =, B =, C = 80 A = 8, B =, C = 78 D) no triangle Find the area of the triangle having the given measurements. Round to the nearest square unit. ) C = 100, a = 5 yards, b = 9 yards A) square yards B) 89 square yards square yards D) square yards

5 Use Heron's formula to find the area of the triangle. Round to the nearest square unit. ) a = 8 inches, b = 1 inches, c = 5 inches A) 1 square inches B) 1 square inches 7 square inches D) 9 square inches Find the product and write the result in standard form. 5) (8 - i) A) 8 - i B) 80 - i - i + 1i D) 8 Perform the indicated operations and write the result in standard form. ) (8 + 9i)( - i) - ( - i)( + i) A) i B) i i D) 15 + i 7) ( + -5) ( + -) A) (1-10 )+ ( + 5)i B) ( )- i + 80i D) i Divide and express the result in standard form. 8) 5 + i 5 - i A) i B) i - 15 i D) i Polar coordinates of a point are given. Find the rectangular coordinates of the point. 9) (-5, -180 ) A) (0, 5) B) (0, -5) (5, 0) D) (-5, 0) 0) (-, 10 ) A), B) -, -, - D) -, The rectangular coordinates of a point are given. Find polar coordinates of the point. Express in radians. 1) (, - ) A), 5 B), 11 8, 11 D) 8, 5 ) (0, - 5) A) (- 5, 90 ) B) (- 5, 70 ) ( 5, 90 ) D) (- 5, 180 ) Write the complex number in rectangular form. ) (cos 10 + i sin 10 ) A) - + i B) + - i i D) + i ) 7(cos + i sin ) A) -7i B) -7 7 D) 7i 5

6 Write the complex number in polar form. 5) A) (cos 0 + i sin 0 ) B) (cos 70 + i sin 70 ) (cos i sin 180 ) D) (cos 90 + i sin 90 ) ) - + i A) cos + i sin cos 5 + i sin 5 B) cos + i sin D) cos 5 + i sin 5 Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form. 7) (cos 0 + i sin 0 )1 A) 1 B) -i i D) -1 8) (- + i) A) - + i B) - i D) - i