2.) Given that sin(θ) = 0.2183 and that θ is in Quadrant I, find the approximation of sin(2θ).
3.) Solve y = sin(2x)sin(x)-cos(2x)-cos(x)+cos(x) on the interval 0Solve this system geometrically (graphically), do not show an algebraic solution. Plot the equation and label the solutions.
Using the Desmos Graphing Calculator or any other graphing calculator, plot one graph that includes the equation and the solution(s). Label the solution(s) with the (x, y) coordinates of the point. Use the software, do not post a hand-drawn graph and do not label point by hand.
14.) The hour hand of my Singing Bird clock is 3.5 inches long and the minute hand is 5 inches long. Find the distance between the ends of the hands when the clock reads four o’clock.
16.) if sin theta =12/13 and pi/2
MATH 108 Midterm This exam is worth 100 points. Questions 1 - 10 are each worth 4 points; do not show your work. Questions 11 – 20 are each worth 6 points; show your work to earn full credit. Leave answers in exact form unless otherwise directed to approximate the results. Write all fractions in lowest form. Round decimals to hundredths unless otherwise directed to round. Write answers using positive exponents except when using scientific notation. Simplify all radicals and rationalize the denominators. Write complex numbers in the form a + bi. Applied problems must have the variables identified (Let x =) and an equation for full credit. Write your answers on the answer sheet provided with this exam. Do not post this exam in the assignment folder. Post only your Answer Sheet in the assignment folder. Fill in the blank. 1.) Convert the angle 72.18° to D°M’S” form. Round the answer to the nearest second. 2.) Given that sin(θ) = 0.2183 and that θ is in Quadrant I, find the approximation of sin(2θ). 3.) Write the equation of a cosine function that has amplitude 3, period 4π, and phase shift . 4.) Find the exact value of . 5.) Write the word “true” or “false.” If the terminal side of θ is in Quadrant IV, then tan(θ) > cos(θ). Select the letter of the one alternative that best completes the statement or answers the question. For multiple choice questions, check that the answers are all letters (A, B, C, D, or E) and not a value. 6.) If θ is an acute angle in a right triangle and measures 19° and the adjacent side measures 7, approximately how long is the hypotenuse? A) B) C) D) E) none of these 7.) Solve for θ in the equation on the interval . A) B) C) D) E) none of these 8.)Solve the triangle with approximate values if β = 37.48°, γ = 32.16°, and c = 3 m. A) a = 3.2 m, b = 2.13 m, α = 110.36° B) a = 3.43 m, b = 5.28 m, α = 110.36° C) a = 5.05 m, b = 3.2 m, α = 110.36° D) a = 3.2 m, b = 5.05 m, α = 110.36° E) none of these 9.) To estimate the height of a unwanted bamboo shoot in his field, a farmer walks off 15 feet from the base of the shoot and estimates the height to be 18 feet. Approximately, what is the angle of elevation the farmer is using from the ground to the top of the shoot for his estimation? A) 39.81° B) 12.68° C) 63° D) 50.19° E) none of these 10.) Debby wants to build a triangular closet under a stairway. The stairway is 18 ft long and its angle of elevation is 35°. Approximately, what will the height of the closet be? A) 10.32 feet B) 14.74 feet C) 14.06 feet D) 29.24 E) none of these SHORT ANSWER. Show your work. The following questions are each worth 6 points. 11.) An airplane is sighted at the same time by two ground observers who are 8 miles apart and both directly east of the airplane. They report the angles of elevation as 14° and 26°. Approximately how high is the airplane? 12.) Solve on the interval . Solve this system geometrically (graphically), do not show an algebraic solution. Plot the equation and label the solutions. Using the Desmos Graphing Calculator or any other graphing calculator, plot one graph that includes the equation and the solution(s). Label the solution(s) with the (x, y) coordinates of the point. Use the software, do not post a hand-drawn graph and do not label point by hand. 13.) A mobile cell tower is 140 feet tall. Approximately how long should a guy wire be if it is to be attached 16 feet from the top and is to make an angle of 38° with the ground? 14.) The hour hand of my Singing Bird clock is 3.5 inches long and the minute hand is 5 inches long. Find the distance between the ends of the hands when the clock reads four o’clock. 15.) Use the sum or difference identity to find the exact value of . 16.) If and find the exact value of . 17.) Approximate the area of a triangle with sides a = 7”, b = 7”, and c = 4”. 18.) Solve the triangle given that b = 0.17 mm and β = 26.7°. Give approximate answers. 19.) Verify: 20.) Verify: 1