# 4th Sample Math Challenge Questions and Answers III( Trigonometry and Combinatorics )

1. What is $\displaystyle\frac{2\pi}{3}$    in degrees?
3. Evaluate: sin14°cos16°+cos14°sin16°
4. Find the length of an arc subtended by an angle of 60° in a circle if the radius is 5cm.
5. Evaluate : sin3150°
6. If sinX=2/3 and X is in second quadrant. What is cosX?
7. The angle of elevation of an object from the top of the tree is 30°. If the height of the tree is 15m. How far is the object from the tree?
8. Twice the supplement of the angle is two more than the compliment of the angle. What is the angle?
9. The length of the diagonal of the rectangle is 20 cm. If the diagonal makes an angle of 30° with the longer side. What is the area of rectangle?
10. Solve for X in (0,360°): 4cos2X-1=0.
11. What is the amplitude and period of the y=2sin3x
12. What is the range of y=3+2sinx?
13. John walked 20m from point A to B. From B he made a left making an angle of 60 degrees with his previous path, after reaching 25 m he decided to go back to point A. How long will he need to walk again?
14. Two sides of triangle measures 6 cm and 10 cm. What is the area of the smallest triangle with integral sides that can be made out of these sides?
15. The angle of elevation of the car from the top tower is 30°. The car travelled with a uniform speed of 20 kph, after 20 minutes the angle of elevation of the car from the top of the tower is 45°. What is the height of the tower?
16. An equilateral triangle is inscribed in a circle, if the radius of the circle is 10cm. What is the area of the triangle?
17.  Jane has 8 shirts and 9 pants. How many clothing combinations does Jane have, if she doesn’t wear 2 specific shirts with 3 specific pants?
18. Out of a classroom of 6 boys and 4 girls the teacher picks a president for the student board, a vice president and a secretary. What is the probability that only girls will be elected?
19. Two dice are rolled. What is the probability the sum will be greater than 10?
20. In Manila, the chance for rain on any given day is 40%. What is the probability that it rains on 5 out of 7 consecutive days in Manila?
21. In how many ways 4 people can be arrange in a circle?
22. How many diagonals does decagon have?
23. How many 3-digit numbers can be formed with the digits 1,4,7,8 and 9 if the digits are not repeated.
24. How many permutations does the word CHACHA have?
25. Given 4 letters and 4 addressed envelopes, in how many ways can the letters be placed in the envelopes so that no letter is in the correct envelope?