Test3Trig

# Test3Trig - on the interval 0 ≤ θ< 2 π Hint Note the...

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Name: MAC 1114 Test 3 11/29/2007 SHOW ALL YOUR WORK. Answers without procedure will be graded zero. [5 pts] 1. Solve the following equation, ﬁnding the exact value of θ in radians, express as fractions of π on the interval 0 θ < 2 π . 3 tan 2 θ = 1 2. Solve each equation, ﬁnding the exact value of θ in radians, express as fractions of π and giving a formula for ALL solutions. [4 pts] a) sin(2 θ - π 2 ) = - 1 [4 pts] b) tan θ 2 = - 1

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3. Solve the following equations, ﬁnding the exact value of θ in radians, express as fractions of π on the interval 0 θ < 2 π . [8 pts] a) sin 2 θ = cos θ [8 pts] b) 1 + sin θ = 2 cos 2 θ [8 pts] 4. Solve the following equation, ﬁnding the exact value of θ in radians, express as fractions of π
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Unformatted text preview: on the interval 0 ≤ θ < 2 π . Hint: Note the equation is of the form a sin θ + b cos θ = c-sin θ + √ 3 cos θ = 1 [3 pts] 5. A security camera in a neighborhood bank is mounted on a wall 9 ft. above the ﬂoor. What angle of depression should be used if the camera is to be directed to a spot 6 ft. above the ﬂoor and 12 ft. from the wall? [5 pts] 6. An aircraft is spotted by two observers who are 1000 feet apart. As the airplane passes over the line joining them, each observer takes a sighting of the angle of elevation to the plane. How high is the airplane? [5 pts] 7. Solve the triangle with α = 30 ◦ , b = 3 and c = 4....
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Test3Trig - on the interval 0 ≤ θ< 2 π Hint Note the...

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