Barsha B.

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Trigonometry

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Question:

find tan495 without using a calculator.

Barsha B.

Answer:

Solution Here 495 is more than a round which is 360 degrees and less than two rounds which is 720 degrees. so, do 495-360=135 Now, look at 135 and always, take a reference to 0 degrees, 180 degrees and 360 degrees. Which one do you think is the nearest from 135? It's obviously, 180. so now take a reference with 180 and write your angle in terms of sum or difference with180 tan135= tan(180-45) Now, which quadrant does 135 lie? It lies in the 2nd quadrant and you have only Sin and its opposite(CSC) positive on that quadrant making rest of others negative so the value we're getting will be negative. And for the value, we look at 45. What is tan45? Yes, It's 1. so tan135 is going to be-1.

Geometry

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Question:

right angle triangle has an exterior angle from a side as 130 degrees such that the 90-degree angle is its nonadjacent angle. find the other nonadjacent angle.

Barsha B.

Answer:

Solution: There are two ways to solve this. First method, the sum of non-adjacent angles is equal to the exterior angle so, 90+X =130 -90 -90 X= 40 degrees answer Second method, the angled interior adjacent to that angle is supplementary to that adjacent angle so that angle will be 180-130=50 degrees. Now, we have two angles of the triangle, and we know that the sum of the angles in triangle is 180 degrees so' 90+50+X=180 140+X=180 combining like terms -140 -140 X=40 degrees answer

Algebra

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Question:

F(x)=X^2 +5X-KX+6,x+3 is the factor of this polynomial. find k.

Barsha B.

Answer:

solution: If F(X) is divisible by X-a, F(a)=0. here, F(X) is divisible by X-3, So, F(3) should be =0 so we obtain an equation f(3)=0 3^2+5(3)-k(3)+6=0 [x substituted with 3] 9+15-3k+6=0 20-3K=0 [combining like terms] -20 -20 -3k=-20 -3k/-3 =-20/-3 [dividing both side by -3] k=-20/3 answer

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