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 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? 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.  #### You've reached the end of your free preview.

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• Fall '13
• SimonRubinstein-Salzedo
• Trigonometry, sinθ
• • •  