
Math
First transform `sin^2(x)` into `1cos^2(x)` and obtain `22cos^2(x)+5cos(x)=4,` `2cos^2(x)5cos(x)+2=0.` This is a quadratic equation for cos(x), the roots are 2 and 1/2. cos(x) never =2....

Math
First transform `cos^2(x)` into `1sin^2(x)` : `22sin^2(x)+7sin(x)=5,` `2sin^2(x)7sin(x)+3=0.` This is a quadratic equation for sin(x), the roots are sin(x)=3 and sin(x)=1/2. The first is...

Math
`cot^2(x)=9,` cot(x)=3 or cot(x)=3. The general solution for cot(x)=a is On `(0, 2pi)` there are `cot^(1)(3), cot^(1)(3)+pi, picot^(1)(3), 2picot^(1)(3).` Note that `cot^(1)(3)=cot^(1)(3).`

Math
This is a quadratic equation for cot(x). There are two roots, cot(x) = 1 and cot(x)=5. Now solve these equations. On `(0, 2pi)` `cot(x)=1` at `x_1=pi/4` and `x_2=(5pi)/4.` Also cot(x)=5 at...

Math
see attached graph. Solutions in the given interval are, x `~~` 0.500 , 0.700 , 2.400 , 2.600

Math
`12sin^2(x)13sin(x)+3=0` using quadratic formula, `sin(x)=((13)+sqrt((13)^24*12*3))/(2*12)` `sin(x)=(13+sqrt(169144))/24` `sin(x)=(13+sqrt(25))/24` `sin(x)=(13+5)/24=3/4,1/3` Solutions of...

Math
`3tan^2(x)+4tan(x)4=0` using quadratic formula, `tan(x)=(4+sqrt(4^24*3*(4)))/(2*3)` `tan(x)=(4+sqrt(16+48))/6` `tan(x)=(4+8)/6=2 , 2/3` solutions for tan(x)=2 for the range...

Math
`tan^2(x)+3tan(x)+1=0` using quadratic equation formula, `tan(x)=(3+sqrt(3^24*1*1))/2` `tan(x)=(3+sqrt(94))/2` `tan(x)=(3+sqrt(5))/2` Solutions for `tan(x)=(3sqrt(5))/2` for the range...

Math
`4cos^2(x)4cos(x)1=0` using quadratic formula, `cos(x)=((4)+sqrt((4)^24*4*(1)))/(2*4)` `cos(x)=(4+sqrt(16+16))/8` `cos(x)=(1+sqrt(2))/2` For cos(x)=`(1+sqrt(2))/2` , No solution since...

Math
`tan^2(x)+tan(x)12=0` using quadratic formula, `tan(x)=(1+sqrt(1^24*1*(12)))/2` `tan(x)=(1+sqrt(49))/2=(1+7)/2=3,4` solutions for tan(x)=3 for the range `0<=x<=2pi` `x=arctan(3) ,...

Math
This is the quadratic equation for tan(x). It has roots 1 and 2. tan(x)=1 on `(0, 2pi)` at `x_1=(3pi)/4` and `x_2=(7pi)/4.` tan(x)=2 on `(0, 2pi)` at `x_3=tan^(1)(2)` and `x_4=pi+tan^(1)(2).`...

Math
`y= sin ((pix)/2) + 1` Before we solve for the xintercepts, let's determine the period of this function. Take note that if a trigonometric function has a form y= Asin(Bx + C) + D, its period...

Math
You need to evaluate the x intercepts of the graph, hence, you need to remember that the graph intercepts x axis at y = 0. Hence, you need to solve for x the equation `y= f(x) = 0` . `sin pi*x +...

Math
xintercepts are points where y=0, so we have to solve the equation `tan^2((pix)/6)3=0.` This implies that `tan((pix)/6)=sqrt(3)` or `tan((pix)/6)=sqrt(3),` and this in turn implies...

Math
xintercepts are the points where y=0. So we have to solve equation `sec^4((pix)/8)4=0,` or `sec^4((pix)/8)=4.` Then `sec^2((pix)/8)=2,` or `sec((pix)/8)=+sqrt(2).` sec(y) = 1/cos(y), therefore...

Math
Solutions of `2sin(x)+cos(x)=0` in the interval (0,2pi) See the attached graph, x `~~` 2.700 , 5.800

Math
See the attached graph Solutions in the given interval are, `x=pi/4 , (3pi)/4, (5pi)/4 , (7pi)/4 , (7pi)/6 , (11pi)/6` `x~~0.800 , 2.300 , 3.600 , 3.900 , 5.500 , 5.800`

Math
See attached graph x=`pi/3 , (5pi)/3` x `~~` 1.000 , 5.200

Math
See the attached graph. Since the equation is undefined for x=pi/2 x=pi/6 , 5pi/6 x `~~` 0.500 , 2.600

Math
see attached graph solutions in the given interval are, x `~~` 0.875 , 3.375

Math
see attached graph Solution in the given interval, x `~~` 4.900

Math
see the attached graph. Solutions in the given interval are, x `~~` 0 , 2.700 , 3.100(pi) , 5.800 , 6.200(2pi)

Math
See the attached graph. Solutions in the given interval are, x `~~` 0.500 , 2.700 , 3.650 , 5.850

Math
See attached graph Solutions in the given interval are, x `~~` 1.000 , 1.750 , 4.125 , 4.875

Math
Find all solutions to the equation `2cos^2(x)+cos(x)1=0` in the interval `[0,2pi).` `2cos^2(x)+cos(x)1=0` `(2cos(x)1)(cos(x)+1)=0` Set each factor equal to zero and solve for the x value(s)....

Math
Solve the equation `2sin^2(x)+3sin(x)+1=0` in the interval [0,2pi). `2sin^2(x)+3sin(x)+1=0` `(2sin(x)+1)(sin(x)+1)=0` Set each factor equal to zero and solve for the x value(s). `2sin(x)+1=0`...

Math
Find all solutions to the equation `2sec^2(x)+tan^2(x)3=0` in the interval `[0,2pi).` `2sec^2(x)+tan^2(x)3=0` Use the pythagorean identity `sec^2(x)=1+tan^2(x)` to substitute in for...

Math
`cos(x)+sin(x)tan(x)=2` `cos(x)+sin(x)(sin(x)/cos(x))=2` `(cos^2(x)+sin^2(x))/cos(x)=2` `1/cos(x)=2` `cos(x)=1/2` General solutions for cos(x)=1/2 are, `x=pi/3+2pin , (5pi)/3+2pin` Solutions for...

Math
`csc(x)+cot(x)=1` `1/sin(x)+cos(x)/sin(x)=1` `1+cos(x)=sin(x)` `1+cos(x)sin(x)=0` `1+cos(x)cos(pi/2x)=0` ` ` `1+2sin((x+pi/2x)/2)sin((pi/2xx)/2)=0` `1+2sin(pi/4)sin(pi/4x)=0`...

Math
`sec(x)+tan(x)=1` `1/cos(x)+sin(x)/cos(x)=1` `1+sin(x)=cos(x)` `1+sin(x)cos(x)=0` `1+cos(pi/2x)cos(x)=0` `1+(2sin((pi/2x+x)/2)sin((xpi/2+x)/2)=0` `1+2sin(pi/4)sin(xpi/4)=0`...

Math
`2cos(2x)1=0,` `cos(2x)=1/2.` The general solution is `2x = +arccos(1/2)+2kpi,` `kinZZ.` Because `arccos(1/2) = pi/3,` the final answer is `x = +pi/6+kpi,` `kinZZ.`

Math
`2sin(2x)+sqrt(3)=0,` `sin(2x) = sqrt(3)/2.` The general solution is `2x = (1)^k*arcsin(sqrt(3)/2)+kpi,` `kinZZ.` Because `arcsin(sqrt(3)/2) = pi/3,` the final answer is...

Math
tan(3x)=1. tan(y) has period `pi` and reaches any value once on each period. We know that `tan(pi/4) = 1,` so `3x = pi/4 + k*pi, kinZZ.` The answer is `x=pi/12 + k*(pi/3), kinZZ.`

Math
`sec(4x)2=0,` `sec(4x)=2.` Because `sec(x)=1/cos(x),` obtain `cos(4x) = 1/2.` The general solution is `4x=+arccos(1/2)+2kpi,` `kinZZ.` `arccos(1/2) = pi/3,` so the final answer is...

Math
`2cos(x/2)sqrt(2)=0,` `2cos(x/2)=sqrt(2),` `cos(x/2) = sqrt(2)/2.` The general solution is: `x/2 = +arccos(sqrt(2)/2) + 2kpi,` `kinZZ.` `arccos(sqrt(2)/2) = pi/4,` so the final answer is: `x =...

Math
`sin(x/2)=sqrt(3)/2.` The general solution is `x/2=(1)^k*arcsin(sqrt(3)/2)+kpi, kinZZ.` So `x=(1)^(k+1)*(2pi/3)+2kpi, kinZZ,` because `arcsin(sqrt(3)/2)=pi/3.`

Math
`tan(3x)tan(x1)=0` solving each part, tan(3x)=0 General solutions for tan(3x)=0 are, `3x=0+pin` `x=(pin)/3` General solutions for tan(x1)=0 are, `x1=0+pin` `x=1+pin` so the solutions are,...

Math
`cos(2x)(2cos(x)+1)=0` solving each part, cos(2x)=0 General solutions for cos(2x)=0 are, `2x=pi/2+2pin , (3pi)/2+2pin` `x=(pi+4pin)/4 , (3pi+4pin)/4` Solving 2cos(x)+1=0, `2cos(x)=1`...

Math
Solve `sin(x)(sin(x)+1)=0` `sin(x)=0` `x=0+pin` `sin(x)+1=0` `sin(x)=1` `x=(3pi)/2+2pin`

Math
Solve the equation `(2sin^2(x)1)(tan^2(x)3)=0` Set each factor equal to zero and solve for the x values. `2sin^2(x)1=0` `2sin^2(x)=1` `sin^2(x)=1/2` `sin(x)=+sqrt(1/2)` `sin(x)=+sqrt(2)/2`...

Math
`cos^3(x)=cos(x)` Let `cos(x)=y` `y^3=y` `y^3y=0` `y(y+1)(y1)=0` solve for y, y=0 , 1 , 1 Therefore cos(x)=0 , cos(x)=1 and cos(x)=1 General solutions for cos(x)=0 are, `x=pi/2+2pin ,...

Math
Solve: `sec^2(x)1=0,[0,2pi)` `tan^2(x)=1` ` ` `tan(x)=+sqrt(1)` `tan(x)=+1` `x=pi/4,x=(3pi)/4,x=(5pi)/4,x=(7pi)/4`

Math
`3tan^3(x)=tan(x)` `3tan^3(x)tan(x)=0` `tan(x)(3tan^2(x)1)=0 =>` `tan(x)=0 , (3tan^2(x)1)=0` General solutions for tan(x)=0 are, `x=0+pin` Solutions in the range `0<=x<=2pi` are, `x=0...

Math
Find all solutions for `2sin^2(x)=2+cos(x)` in the interval [0, `2pi).` Use the pythagorean identity `sin^2(x)+cos^2(x)=1.` Solve for `sin^2(x)` and the pythagorean identity would be...

Math
Solve the equation `sec^2(x)sec(x)=2,[0,2pi).` `sec^2(x)sec(x)2=0` `(sec(x)2)(sec(x)+1)=0` Set each factor equal to zero and solve for the x values. `sec(x)2=0` `sec(x)=2` `cos(x)=1/2`...

Math
`sec(x)csc(x)=2csc(x)` `sec(x)csc(x)2csc(x)=0` `csc(x)(sec(x)2)=0` `csc(x)=0 , sec(x)=2` No solutions for x for csc(x) in the range `0<=x<=2pi` General solutions for sec(x)=2 are...

Math
`2sin(x)+csc(x)=0` `2sin(x)+1/sin(x)=0` `(2sin^2(x)+1)/sin(x)=0` solving above , `2sin^2(x)+1=0` `2sin^2(x)=1` `sin^(2)x=1/2` `sin(x)=+i/sqrt(2)` Solutions for the range `0<=x<=2pi` No...

Math
`sin(x)2=cos(x)2` `sin(x)2cos(x)+2=0` `sin(x)cos(x)=0` `(sin(x)cos(x))/cos(x)=0` `tan(x)1=0` `tan(x)=1` General solutions for tan(x)=1 are `x=pi/4+pin` Solutions for the range...

Math
Solve the equation: `sqrt(3)csc(x)2=0` `csc(x)=2/sqrt(3)` Since sin(x) and csc(x) are reciprocal functions `sin(x)=sqrt(3)/2` `x=pi/3+2pin` `x=(2pi)/3+2pin`

Math
`tan(x)+sqrt(3)=0` ` ` `tan(x)=sqrt(3)` `x=(2pi)/3+pin` General solution for x,