trigonometry math Questions and Answers

trigonometry math

The most straightforward way to obtain the expression for cos(2x) is by using the "cosine of the sum" formula: cos(x + y) = cosx*cosy - sinx*siny. To get cos(2x), write 2x = x + x. Then, cos(2x) =...

Latest answer posted February 19, 2018, 3:58 pm (UTC)

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trigonometry math

We need to simplify the expression (cos (x-y))^2 + (cos (x+y))^2 - cos 2x *cos 2y (cos (x-y))^2 + (cos (x+y))^2 - cos 2x *cos 2y => (cos x * cos y + sin x * sin y)^2 + (cos x * cos y - sin x *...

Latest answer posted April 4, 2011, 3:29 am (UTC)

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trigonometry math

We have to verify sin 25 + sin 35 = cos 5 sin 25 + sin 35 => 2* sin (25 + 35)/2 * cos 10/2 => 2* sin (60)/2 * cos 5 => 2* sin 30 * cos 5 sin 30 = 1/2 => 2 * (1/2) cos 5 => cos 5 This...

Latest answer posted March 8, 2011, 1:44 am (UTC)

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trigonometry math

Since this trigonometric sum involves the angles that are multiples of pi/3 (equivalent to 60 degrees)—a "special" angle with known sine, cosine, and tangent values—each of the terms can be...

Latest answer posted August 21, 2018, 12:21 pm (UTC)

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trigonometry math

Here, we use the relations that tan x = sin x / cos x. sin (a + b) = sin a * cos b + cos a * sin b cos ( a+ b) = cos a * cos b - sin a * sin b tan (a + b) = sin (a + b) / cos ( a + b) => [sin a...

Latest answer posted January 23, 2011, 11:32 pm (UTC)

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trigonometry math

We have to find the zeros of f(x) = sin x + cos x f(x) = sin x + cos x = 0 => sin x = -cos x => tan x = -1 x = arc tan (-1) In the interval (0, pi) , x = -pi/4 + pi = 3*pi/4 The required...

Latest answer posted March 7, 2011, 8:59 pm (UTC)

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trigonometry math

We have sin a + cos a = 1/3 Use the fact that sin 2a = 2*(sin a)(cos a) sin a + cos a = 1/3 square the right and left hand sides (sin a + cos a)^2 = (1/3)^2 => (sin a)^2 + (cos a)^2 + 2*(sin...

Latest answer posted April 7, 2011, 3:32 am (UTC)

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trigonometry math

We are asked to show that (sin3a+sina+sin5a)/(cos3a+cosa+cos5a)=tan3a. Note that sin3a=sina(-1+4cos^2a) and sin5a=sina(1-12cos^2a+16cos^4a)Similarly cos3a=cosa(1-4sin^2a) and...

Latest answer posted June 27, 2019, 7:17 am (UTC)

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trigonometry math

Another way of solving the problem (cos x)² - (sin x)² = 2(cos x)² - 1 is as follows: Consider the right-hand side (RHS) of the equation: 2(cos x)² - 1 From the Pythagorean Identity, we know that...

Latest answer posted March 26, 2018, 9:37 am (UTC)

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trigonometry math

We have to find x given that : tan^2 x - 4sec x + 5 = 0 (tan x)^2 - 4sec x + 5 = 0 => ( 1 - (cos x)^2)/( cos x)^2) - 4/ cos x + 5 = 0 let cos x = y => (1 - y^2)/y^2 - 4/y + 5 = 0 => (1 -...

Latest answer posted February 27, 2011, 12:59 am (UTC)

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trigonometry math

We have sin (a+b) = (sin a * cos b + cos a * sin b) and cos(a + b) = (cos a * cos b – sin a * sin b) Also tan (a + b) = [sin (a+b)] / [cos (a+b)] => [sin a * cos b + cos a * sin b] / [cos a *...

Latest answer posted January 17, 2011, 12:56 pm (UTC)

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trigonometry math

First, let us rewrite the cube of sine and cosine in the left-hand side of the above equation as a product of a square of the sine/cosine and the sine/cosine: (sinx)^2*sinx*sin(3x) +...

Latest answer posted July 30, 2018, 5:26 pm (UTC)

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trigonometry math

We are given that sin x = (1/2) and sin y =(1/3). We have to find tan ( x - y). sin x = (1/2) => tan x = (1/2)/ sqrt [1 - (1/2)^2] => (1/2)/ sqrt (3/4) => 1/ sqrt 3 sin y = (1/3) => tan...

Latest answer posted January 31, 2011, 4:12 pm (UTC)

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trigonometry math

To find the distance from the vertex to the shoreline which will divide the lot into two equal parts, find the length of what would be the line dividing the lot. As we have 2 exisitng angles, find...

Latest answer posted October 21, 2013, 9:30 am (UTC)

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trigonometry math

The expression you have provided is true because sin 2x = 2*sin x*cos x and cos 2x = (cos x)^2 - (sin x)^2 Let start with (cos x + sin x)/(cos x - sin x) multiply the numerator and denominator by...

Latest answer posted June 20, 2011, 1:36 pm (UTC)

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trigonometry math

We have to prove that cos 2x * (1 + tan x*tan 2x) = 1 cos 2x = 1 - (sin x)^2 and tan 2x = 2*tan x/(1 - (tan x)^2) cos 2x * (1 + tan x*tan 2x) => ((cos x)^2 - (sin x)^2)*(1 + (tan x)*(2*tan x/(1...

Latest answer posted July 2, 2011, 10:47 pm (UTC)

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trigonometry math

We have to determine the trigonometric form of z = -2i The absolute value of z = -2i sqrt [ 0^2 + (-2)^2] => sqrt 4 => 2 and the the argument is -90 as the real component is zero. Therefore...

Latest answer posted January 29, 2011, 1:50 am (UTC)

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trigonometry math

We need the solutions of sin 12x + cos 6x = 0. sin 12x + cos 6x = 0 => 2*sin 6x*cos 6x + cos 6x = 0 let cos 6x = y => 2*sqrt(1 - y^2)*y + y = 0 => y(2*sqrt(1 - y^2) + 1) = 0 => y = 0...

Latest answer posted February 27, 2011, 1:19 am (UTC)

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trigonometry math

We have to solve 3*cos(3x - 1) = 0 for x. 3*cos(3x - 1) = 0 => cos(3x - 1) = 0 => 3x - 1 = arc cos 0 => 3x - 1 = pi/2 + 2*n*pi and 3x - 1 = 3*pi/2 + 2*n*pi => 3x = pi/2 +1 + 2*n*pi and...

Latest answer posted March 10, 2011, 11:54 pm (UTC)

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trigonometry math

sin (x + y) = sin x* cos y + cos x * sin y It is given that sin x + cos y = 1/4 and cos x + sin y = 1/2 sin x + cos y = 1/4 square the two sides => (sin x)^2 + (cos y)^2 + 2*sin x*cos y = 1/16...

Latest answer posted May 6, 2011, 5:41 pm (UTC)

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trigonometry math

We have that tan x = 6/11. tan x is equal to the opposite side/ adjacent side for the angle in a right triangle. Using the Pythagorean theorem we calculate the length of the hypotenuse as sqrt (...

Latest answer posted January 31, 2011, 3:44 pm (UTC)

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trigonometry math

We have to solve 1 + cos x + cos 2x = 0 for x in the interval (0, pi) 1 + cos x + cos 2x = 0 => 1 + cos x + 2(cos x)^2 - 1 = 0 => cos x + 2(cos x)^2 = 0 => cos x( cos x + 2) = 0 => cos...

Latest answer posted May 11, 2011, 6:29 am (UTC)

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trigonometry math

We have to simplify: [cos x*sin(2x) - 2 sin x]/(sin x)^2 *cos x [cos x*sin(2x) - 2 sin x]/(sin x)^2 *cos x use sin 2x = 2*sin x * cos x => [2*(cos x)^2 *sin x - 2 sin x]/(sin x)^2 *cos x...

Latest answer posted March 3, 2011, 12:21 am (UTC)

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trigonometry math

We have 2*sin x*sin 3x - cos 4x = 0 (sin a)(sin b) = (1/2)(cos (a - b) - cos (a + b)) => 2*(sin a)(sin b) = cos (a - b) - cos (a + b) 2*sin x*sin 3x - cos 4x = 0 => cos (x - 3x) - cos 4x -...

Latest answer posted May 17, 2011, 12:24 am (UTC)

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trigonometry math

We have to find the sum sin 135 + cos 150 Use the relations: sin (90 + x) = cos x and cos(180 - x) = -cos x sin 135 + cos 150 => sin (90 + 45) + cos (180 - 30) => cos 45 - cos 30 cos 45 =...

Latest answer posted June 12, 2011, 2:31 am (UTC)

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trigonometry math

We have to determine the solutions for cos 2a = sqrt( 1 - sin a)^2, lying in the range 0<a<180 cos 2a = sqrt( 1 - (sin a)^2) => cos 2a = sqrt ( (cos a)^2) => cos 2a = cos a => 2*(cos...

Latest answer posted February 22, 2011, 2:32 am (UTC)

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trigonometry math

We have to show that cos 3B + cos B = 2(cos 2B)* cos B We use the relations: cos 2B = 2*(cos B)^2 - 1 and cos 3B = 4(cos B)^3 - 3cos B We start with the left hand side cos 3B + cos B => 4(cos...

Latest answer posted February 21, 2011, 5:03 pm (UTC)

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trigonometry math

We have to solve cos 3x = cos x for x in the interval (0 , 2*pi) We know that cos 3x = 4(cos x)^3 - 3cos x cos 3x = cos x => 4(cos x)^3 - 3cos x = cos x let cos x = t => 4t^3 - 4t = 0 =>...

Latest answer posted February 21, 2011, 1:49 am (UTC)

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trigonometry math

The equation given is 99sin^2x-101=-sin^2x. The number of roots of the equation have to be determined. 99(sin x)^2 - 101 = -(sin x)^2 => 100(sin x)^2 = 101 => (sin x)^2 = 101/100 => sin x...

Latest answer posted April 18, 2011, 1:42 am (UTC)

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trigonometry math

The equation to be solved is (cos x)^6 = 1 - (sin x)^6 (cos x)^6 = 1 - (sin x)^6 => (cos x)^6 + (sin x)^6 = 1 => (cos x)^2^3 + (sin x)^2^3 = 1 use a^3 + b^2 = (a + b)(a^2 - ab + b^2) =>...

Latest answer posted April 18, 2011, 2:57 am (UTC)

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trigonometry math

We have to prove: (sqrt (1 - (cos t)^2) * sqrt ((sec t )^2) - 1)) / cos t = (tan t)^2 (sqrt (1 - (cos t)^2) * sqrt ((sec t )^2) - 1)) / cos t => (sqrt (sin t)^2 * sqrt ( 1/ (cos t)^2) - 1) / cos...

Latest answer posted January 23, 2011, 3:56 am (UTC)

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trigonometry math

To prove the identity: AB^2+AC^2=2BM^2+2AM^2, we have to use the law of cosines. For the triangle AMB, c^2 = x^2 + y^2 - 2*x*y*cos (AMB)...(1) For the triangle AMC b^2 = x^2 + y^2 - 2*x*y*cos...

Latest answer posted January 26, 2011, 6:05 pm (UTC)

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trigonometry math

We have to prove that (sin x)^2 * [ 1 + (cot x)^2] = 1 (sin x)^2 * [ 1 + (cot x)^2] => (sin x)^2 * [ 1 + (cos x)^2/ (sin x)^2] => (sin x)^2 * [ (sin x)^2 + (cos x)^2]/ (sin x)^2 => (sin...

Latest answer posted March 3, 2011, 12:25 am (UTC)

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trigonometry math

We have to solve 2 tan x - 1 = -tan (-x) Now we know that tan -x = - tan x 2 tan x - 1 = -tan (-x) => 2 tan x - 1 = tan (x) => tan x - 1 = 0 => tan x = 1 => x = arc tan 1 => x = 45...

Latest answer posted January 20, 2011, 4:40 pm (UTC)

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trigonometry math

The equation that has to be solved is (sin B)^2- 3 sin B + 2 =0 where 0 ≤ B ≤ 2π. (sin B)^2- 3*sin B +2 =0 => (sin B)^2- 2*sin B - sin B +2 =0 => (sin B)(sin B - 2 ) - 1( sin B - 2) =0 =>...

Latest answer posted March 8, 2011, 11:59 am (UTC)

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trigonometry math

We have to identify t if cos 2x + 2*(sin x )^2 + t = 0 cos 2x + 2*(sin x )^2 + t = 0 use cos 2x = 1 - 2*(sin x)^2 => 1 - 2*(sin x)^2 + 2*(sin x)^2 + t = 0 => 1 + t = 0 => t = -1 The...

Latest answer posted March 21, 2011, 4:51 pm (UTC)

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trigonometry math

We have to find x if (sin x)^2 = 1/4 (sin x)^2 = 1/4 => sin x = 1/2 and sin x = -1/2 x = arc sin (1/2) and x = arc sin (-1/2) arc sin (1/2) = 30 degrees and arc sin (-1/2) = -30 degrees. As the...

Latest answer posted April 14, 2011, 6:45 am (UTC)

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trigonometry math

We have to prove that 1+ sin x = cos( 90 - x) + cot 45 Let's start with cos( 90 - x) + cot 45 cos (90 - x) - cot 45 cos 45 = sin 45 = 1/sqrt 2 , cos (90 - x) = sin x => sin x + cot 45 => sin...

Latest answer posted March 13, 2011, 1:58 am (UTC)

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trigonometry math

We have a right triangle with A = 90 degrees and we have to calculate cos B / sin C + cos C / sin B Let's take the sides opposite angle A as a, that opposite angle B as b and that opposite angle C...

Latest answer posted January 31, 2011, 9:30 pm (UTC)

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trigonometry math

We are given that 1 - 2(sin a)^2 = 2* (cos a)^2 + m. We have to find m. 1 - 2(sin a)^2 = 2* (cos a)^2 + m => 1 - 2(sin a)^2 - 2* (cos a)^2 = m => 1 - 2[(sin a)^2 + (cos a)^2] = m now use (sin...

Latest answer posted January 31, 2011, 9:35 pm (UTC)

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trigonometry math

We have to find x for 100*sin x - 99*cos x = 0 100*sin x - 99*cos x = 0 => 100*sin x = 99*cos x => sin x / cos x = 99/100 => tan x = 99/100 => x = arc tan(99/100) => x = 44.71...

Latest answer posted March 3, 2011, 4:59 pm (UTC)

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trigonometry math

We have to prove that (tan t)^4 + (tan t)^2 + 1 = (1 - (sin t)^2* (cos t)^2) / (cos t)^4 The left hand side: (tan t)^4 + (tan t)^2 + 1 => (sin t)^4 / (cos t)^4 + (sin t)^2 / (cos t)^2 + 1 =>...

Latest answer posted January 23, 2011, 3:42 am (UTC)

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trigonometry math

We have to prove that (csc x)^2 = (2 sec 2x) / (sec 2x - 1) (2 sec 2x) / (sec 2x - 1) => [2*(1/ cos 2x)] / [((1/ cos 2x) - 1)] => [2*(1/ cos 2x)] / [((1 - cos 2x)/ cos 2x)] => 2/ (1 - cos...

Latest answer posted January 23, 2011, 3:49 am (UTC)

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trigonometry math

We are given that sin x = 1/4 and cos x = 3/4. We have to find sec 2x. sec 2x = 1/ cos 2x cos 2x = (cos x)^2 - (sin x)^2 => (3/4)^2 - (1/4)^2 => (9 - 1)/ 16 => 8/ 16 => 1/2 So sec 2x = 2

Latest answer posted January 20, 2011, 11:59 pm (UTC)

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trigonometry math

We have to find the value of [tan (pi/ 7) + cot (pi/2 - pi/6)] / (1+ tan (-pi/7)*tan (pi/6)) We know that cot (pi/2 - pi/6) = tan (pi/6) and as tan is odd tan (-x) = -tan x Also, tan (a + b) =...

Latest answer posted January 22, 2011, 3:49 am (UTC)

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trigonometry math

We have sin x/ cos x = 2 We need to find (cos x)^2 sin x/ cos x = 2 => 2*sin x*cos x = 4*(cos x)^2 => sin 2x = 4*(cos x)^2 => (cos x)^2 = (sin 2x)/4 The value of (cos x)^2 = (sin 2x)/4

Latest answer posted April 19, 2011, 8:37 am (UTC)

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trigonometry math

We have to verify sin x < 1 / 2 cos x. sin x < 1 / 2 cos x => 2 sin x * cos x < 1 => sin 2x < 1 But sin 2x can also be equal to 1. Note: Therefore the inequality should be sin x...

Latest answer posted January 26, 2011, 12:31 am (UTC)

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