MATH225 final.docx - Exam 1 1 360 °−300 °=60 °= Write equation of the circle centered at(3-10 and sin � 300°)= passing through-1-6 r 2= x−h)2

MATH225 final.docx - Exam 1 1 360 °−300 °=60 °= Write...

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Exam 1 1. Write equation of the circle centered at (3, -10) and passing through (-1,-6) r 2 = ( x h ) 2 + ( y k ) 2 r 2 = [ 3 ( 1 1 ) ] 2 + [ 10 ( 6 ) ] 2 r 2 = 4 2 +(− 4 ) 2 r 2 = 16 + 16 = 32 Ans : ( x 3 ) 2 + ( y + 10 ) 2 = 32 2.At what point of the first quadrant does the line with equation y=x+2 intersect the circle with radius 6 and center (0,2)? 3. On a circle of radius 5 miles, find the length of an arc that subtends a central angle of 3 radius. 5 ( 3 ) = 15 mi 4. A sector of a circle has a central angle of 45 degrees. Find the area of the sector if the radius of the circle is 9 cm. π ( r ) 2 × 45 ° 360 ° π ( 9 ) 2 × 45 360 Ans :31.8086 c m 2 5. For an angle of 5 π 3 radians, give the reference angle and which quadrant the angle lies in. Then compute the sine and cosine of the angle. 5 π 3 × 180 π = 300 ° = 4 th quadrant 360 ° 300 ° = 60 ° = π 3 sin ( 300 ° )= 3 2 cos ( 300 ° )= 1 2 6. Give an angle with 0 ° < θ < 360 ° that has the same sine value as 70 ° . (answer cannot be 70 ° ) 110 ° 180 ° 70 ° = 110 ° 7. Find the exact value of the 6 trig functions for an angle of 3 π 4 3 π 4 = 3 π 4 × 180 π = 135 ° 180 ° 135 ° = 45 ° sin ( 135 ° ) = 2 2 ,csc ( 135 ° ) = 2 cos ( 135 ° ) = 2 2 ,sec ( 135 ° ) = 2 2 tan ( 135 ° ) =− 1,cot ( 135 ° ) =− 1 8. Prove the identity: csc 2 x sin 2 x cscx + sinx = cosxcotx csc 2 x sin 2 x cscx + sinx = ( cscx + sinx ) ( cscx sinx ) cscx + sinx = 1 sinx sinx 1 ( sinx sinx ) = ( 1 sinx sinx ) = cos 2 x sinx cosxcotx = cosx ( cosx sinx ) = cos 2 x sinx 9. In a right triangle with legs a=6ft and b=8ft, and angle A opposite side a, fine the 6 trig functions of angle A. r 2 = 6 2 + 8 2 r = 10
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sin = 6 10 = 3 5 ,csc = 5 3 a=6 c=10 cos = 8 10 = 4 5 ,sec = 5 4 tan = 6 8 = 3 4 , cot = 4 3 b=8 10.A 40-ft ladder leans against a building so that the angle between the ground and the ladder is 80 degrees. How high does the ladder reach up the side of the building?
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1. Sketch one period of f(x)=-2cos(2x)+1 and label 5 key points(beginning and ending of one period, halfway across the period, and ¼ and ¾ of the way across the period) Amp: 2 ; per: 2 π 2 = π vertical shirt: 1 up range 2[-1,1] +1 = [-1,2]+1 =[-1,3] Mid line:y=1 3 2 1 y=1 -1 2. For the function y = 4sin 3 ( x π 6 ) 5 , give the amplitude, period, horizontal shift, and midline.
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  • Fall '13
  • SimonRubinstein-Salzedo
  • Trigonometry, sinθ

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