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Trigonometry Review Problems The following problems are provided as examples of some of the trigonometry concepts and topics that are tested on the mathematics placement test used at UNCW. They are not intended to be a complete summary of all topics covered on the test or representative of prerequisite material for any UNCW mathematics course. See our website (www.uncw.edu/math) for more information about the placement test. 1. State the value of each of the following: e.) sin 225 a.) sin 30 b.) cos6 f.) csc 23 c.) tan 135 g.) cot 0 d.) sec h.) cos176 2. If is an acute angle and sin 23 , find the value of each of the following: a.) cos 3. If sin b.) tan 1 2 a.) sin 2 and cos 3 2 c.) sec d.) csc , find the value of each of the following: b.) cos2 c.) tan 4. In triangle ABC, the measures of angles A, B, and C are 20 , 70 , and 90 , respectively. If BC is 8 units long, how long is AC ? 5. In triangle ABC, angle C is a right angle. Let the measure of angle A be and the measure of angle B be . Let the side opposite angle A have length a, the side opposite angle B have length b, and the hypotenuse have length c. Find each of the following: a.) cos 6. b.) tan tan c.) sin d.) sin 2 1 1 equals 1 sin( x) 1 sin( x) 7. In triangle ABC, angle at C is a right angle. The measure of angle A is , and the length of side AC is 1. If 45 60 , then what are the possible lengths of side BC ? 8. If tan 3 4 and 2 , then what is the value of cos ? 9. If 2 sin 2 3 sin 1 0 and 0 2 , then what are the possible values of ? 10. If sin 1 and 0 2 , then what are the possible values of ? 11. In right triangle ABC (with right angle at C), the hypotenuse has length 5. The side opposite angle A has length 2. If the measure of angle A is , what is sec ? 12. What is the period of the graph of the function f ( x) 13 sin 2 x ? 13. The lengths of the two legs of a right triangle are 3 cos and 3 sin . How long is the hypotenuse? 14. What is the angle of elevation to the top of a building 200 feet tall from a point 12 feet from the base of the building? ? 15. What is the exact value of 3 sin 12 ANSWERS 3 2 b.) c.) d.) e.) 1 1 2 2 2 3 f.) g.) undefined h.) 23 2. a.) 5 3 b.) 2 5 5 c.) d.) 3 5 5 3 2 3. a.) b.) 1 2 c.) 4. 5. 3 2 3 3 8 tan 70 or 8 / tan 20 a.) bc b.) 1 c.) a 2 b 2 / c 2 d.) 2ab / c 2 1 2 1. a.) 6. 2 sin( x) cos 2 ( x) 7. 1 BC 3 8. 54 9. 7 6 10. 2 11. 5 21 21 , 11 6 , or 3 2 12. 13. 3 14. arctan 503 15. 3 2 2 3