Exam is: Math Dr. Smithies Spring 2018 Review and Practice Test 3

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1 Math Dr. Smithies Spring 2018 Review and Practice Test 3 Test 3 is Tuesday March 24 th. Unless you have documentation of a University Approved Excuse, you may not be able to take a make-up exam for full credit. So please make every effort to be at the test on time and ready to work. You will need a calculator and pencils but no scratch paper or formula sheets. Our formula sheet (page 252 of our book) will be provided. Test 3 will cover Sections 2.4, 2.5, 3.1, 3.2 Θ Cos Θ Sin Θ Θ Cos Θ Sin Θ Θ Cos Θ Sin Θ Θ Cos Θ Sin Θ (4) 2. Our Final Exam is: Day: Date: Time: Place: Our final exam is a block final, meaning this same test is given at the same time to all sections of Trigonometry. If you arrive at our final exam late, you might not be able to submit a final exam. You must have photo ID to submit a final exam. To earn a grade of C or higher in this class, you must score 50 percent or higher on our final exam.

2 Math Practice Test for Sections 2.4, 2.5, 3.1, 3.2 Page 2 of 5 (8)3. Given and find the exact value of cos u v. ( ) (8)4. Given that, find the exact value of,, and. (4)5. Verify that the given equation is an identity. cos x y 1 tan x tan y cos xcos y

3 Math Practice Test for Sections 2.4, 2.5, 3.1, 3.2 Page 3 of 5 (8)6. Given that 3 u sin u, u, state the quadrant in which lies. Find the exact value of Quadrant: u sin 2 (12)7. Use product-to-sum or sum-to-product identities to find the exact value of the expressions. a) b)

4 Math Practice Test for Sections 2.4, 2.5, 3.1, 3.2 Page 4 of 5 (6)8. True/False. Circle T or F. T F a) If triangle ABC has standard labeling and the measures of b, c, and A are shown, then SSA is given. T F b) If triangle ABC has standard labeling and the measures of b, c, and A are shown, then the Law of Cosines can be applied to solve the triangle. T F c) There is one unique triangle ABC with measures A 140, B 15, and b 7. (10)9. Which of the following sets of data determines a unique triangle? A) A 50, B 50, C 80 B) a 5, b 13, c 15 C) a 11, b 5, c 4 D) A 50, B 30, C 70 (4)10. Which one of the following triangles can be solved using the Law of Sines but not the Law of Cosines? A) You are given the measure of all three sides. B) You are given the measure of all three angles. C) You are given the measure of two angles and the side between them. D) You are given the measure of two sides and the angle between them.

5 Math Practice Test for Sections 2.4, 2.5, 3.1, 3.2 Page 5 of 5 For problems 11 and 12, round your answers to the nearest tenth. (10)11 Determine the angle θ in the design of the streetlight shown in the figure, where x = 2.5 (Round your answer to one decimal place.) Angle θ = (14)12. Use the Law of Sines to solve the triangle. If no solution exists, state why. If two solutions exist, solve both (Round your answer to one decimal place.)

6 Math Dr. Smithies Spring 2018 Review and Practice Test 3 Test 3 is Tuesday March 24 th. Unless you have documentation of a University Approved Excuse, you may not be able to take a make-up exam for full credit. So please make every effort to be at the test on time and ready to work. You will need a calculator and pencils but no scratch paper or formula sheets. Our formula sheet (page 252 of our book) will be provided. Test 3 will cover Sections 2.4, 2.5, 3.1, 3.2 Θ Cos Θ Sin Θ THE SOLUTION TO THIS IS POSTED ON OUR CLASS Θ Cos Θ Sin Θ WEBSITE BE ABLE TO QUICKLY GIVE THE VALUES OF ANY OF OUR 6 TRIG FUNCTIONS AT ALL MULTIPLES OF AND. (OUR 16 ANGLES). Θ Cos Θ Sin Θ Θ Cos Θ Sin Θ (4) 2. Our Final Exam is: Day: Wednesday Time: 3:15 5:30 PM Date: May 9 th Place: To Be Announced (TBA) Our final exam is a block final, meaning this same test is given at the same time to all sections of Trigonometry. If you arrive at our final exam late, you might not be able to submit a final exam. You must have photo ID to submit a final exam. To earn a grade of C or higher in this class, you must score 50 percent or higher on our final exam.

7 Solutions Math Practice Test for Sections 2.4, 2.5, 3.1, 3.2 Page 2 of 5 (8)3. Given and find the exact value of cos a b c u By the Pythagorean theorem From our formula sheet ( ). We are given u is in quadrant II, so cos(u) is negative. Similarly, since v is in quadrant II, sin(v) is positive. u v. ( ). You could note the triangle with angle v is By the Pythagorean theorem ( ) ( ). You could note the triangle with angle u is ( ) ( ) ( ) ( ) ( ) (8)4. Given that, find the exact value of,, and. You could actually deduce since is in quadrant II and its Sine is, that. This makes This immediately gives the double angle values but the intended solution is to use our formula sheet. First note that since is in quadrant II, is negative. Thus, ( ),. So, ( ) ( ) ( ) ( ). cos x y (4)5. Verify that the given equation is an identity: 1 tan x tan y. cos xcos y There are many options. We substitute the angle sum formula for cosine in. ( )

8 Math Practice Test for Sections 2.4, 2.5, 3.1, 3.2 Page 3 of 5 3 u (8)6. Given that sin u, u, state the quadrant in which lies. Find the exact value of Multiply the given inequality, through by. This gives us. So, is in quadrant I. This means all six trig functions are positive on. From our formula sheet,. We take the positive root as explained above. From the Pythagorean theorem. Now is in quadrant II, so is negative. Thus, ( ) So, (12)7. Use product-to-sum or sum-to-product identities to find the exact value of the expressions. a) From the formula sheet ( ) ( ). Here. ( ) ( ) ( ) ( ) [ ]. b) From the formula sheet ( ) ( ) ( ) ( ) Here. So, ( ) ( ) ( ) ( ) ( ) ( ) This simplifies as ( ) ( ) ( ) ( ) ( ) ( )

9 Math Practice Test for Sections 2.4, 2.5, 3.1, 3.2 Page 4 of 5 (6)8. True/False. Circle T or F. F a) If triangle ABC has standard labeling and the measures of b, c, and A are shown, then SSA is given. [That is SAS given.] T b) If triangle ABC has standard labeling and the measures of b, c, and A are shown, then the Law of Cosines can be applied to solve the triangle. T c) There is one unique triangle ABC with measures A 140, B 15, and b 7. [C = 180 A B. The data AAA gives the shape of ABC; b= 7 fixes the size.] (10)9. Which of the following sets of data determines a unique triangle? A) A 50, B 50, C 80 B) a 5, b 13, c 15 This is AAA there are Start by finding the angle infinitely many such triangles. opposite the largest side. ( )( ) -1 and 1. So there is no such triangle.. This is not between C) a 11, b 5, c 4 D) A 50, B 30, C 70 You can use the law of cosines to get A, B, and C. There is only 1 such triangle. These angles do not add to 180. No such triangle. (4)10. Which one of the following triangles can be solved using the Law of Sines but not the Law of Cosines? A) You are given the measure of all three sides. [No. Need Law of Cosines.] B) You are given the measure of all three angles. [No AAA is not solvable.] C) You are given the measure of two angles and the side between them. [Yes. Need Law of Sines.] D) You are given the measure of two sides and the angle between them.. [No. Need Law of Cosines.]

10 Math Practice Test for Sections 2.4, 2.5, 3.1, 3.2 Page 5 of 5 For problems 11 and 12, round your answers to the nearest tenth. (10)11 Determine the angle θ in the design of the streetlight shown in the figure, where x = 2.5 (Round your answer to one decimal place.) So ( ) ( )( ) (14)12. Use the Law of Sines to solve the triangle. If no solution exists, state why. If two solutions exist, solve both (Round your answer to one decimal place.) This is essentially Take-home Quiz 7. See the solution for Quiz 7.