# Questions on Algebra: Trigonometry answered by real tutors!

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 Question 672037: determine the number of possible solutions for each triangle. A= 42 degrees, a=22, b=12 Click here to see answer by stanbon(60778)

 Question 672115: use the half angle formula to find the exact values of tan 3pi/8 Click here to see answer by nerdybill(7090)

 Question 672286: Express in the form a+bi, where a and b are real numbers. 4(cos(pi/4) + isin(pi/4)) Click here to see answer by ewatrrr(11176)

 Question 672290: express in the form a+bi, where a and b are real numbers 8(cos(7pi/4) + isin(7pi/4)) Click here to see answer by ewatrrr(11176)
 Question 672290: express in the form a+bi, where a and b are real numbers 8(cos(7pi/4) + isin(7pi/4)) Click here to see answer by solver91311(18785)

 Question 672297: If tan(t)=x and t is in quadrant I, how would you use a right triangle to find expressions for sin(t) and cos(t) in terms of x? Click here to see answer by lwsshak3(7679)

 Question 672379: Suppose v is in the interval (0, pi/2) with tan v=11 Find exact expression for the indicated quantity. Click here to see answer by stanbon(60778)

 Question 671982: explain how the exact value of sin 75* can be found using either sin(a+b)=sin a cos b + cos a sin b or sin(a-b)= sin a cos b-cos a sin b Click here to see answer by lwsshak3(7679)

 Question 671967: Use a graph to solve the equation on the interval [-2π, 2π]. TanX = 1 And TanX = √3 Click here to see answer by lwsshak3(7679)

 Question 672385: Suppose u is in the interval (0, pi/2) with tan u=8 Find exact expression for csc u. Click here to see answer by stanbon(60778)

 Question 671952: Solve the equation for solutions over the interval [0,2pi) cot^2 theta= (-5) +4csc theta I believe I have solved to the last step which is where I am stuck. This is what I have done so far (please forgive all the steps if I do not do them I will get lost and not understand what happened along the way): 0= (-5) +4csc theta - csc^2 theta +1 0= (-5) + 1 + 4csc theta - csc ^2 theta 0= (-4) + 4csc theta - csc^2 theta 0= -csc^2 theta + 4csc theta - 4 0= (csc theta -2)(csc theta +2) Set both to zero: csc theta-2 = 0 csc theta = 2 (this is where I am stuck...what next?) csc theta+2=0 csc theta = -2 (again stuck here) Thank you in advance :) Click here to see answer by lwsshak3(7679)

 Question 672462: Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) 3 tan^3theta = tan theta Click here to see answer by swincher4391(733)

 Question 672466: Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) 3 tan^3theta = tantheta Click here to see answer by lwsshak3(7679)

 Question 672314: An equation is given. (Enter your answers as a comma-separated list. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) − 2/sqr3 cos 3θ = 1 (a) Find all solutions of the equation. (b) Find the solutions in the interval [0, 2π). Click here to see answer by lwsshak3(7679)

 Question 672541: If cos beta = 0.6, find without using tables, the value of a) sin beta b) 1- cos^2 beta Click here to see answer by Alan3354(34679)

 Question 672588: Can you help me to solve Trig equations algebraically? 3tan^3(t)-3tan^2(t)-tan(t)+1=0 What I have so far, if correct;I changed my tan(t) to (x) for less confusion [3tan^3(t)-3tan^2(t)] -tan(t)+1=0 (3x^3-3X^2)-1x+1 = 0 3x(x^2-x)-1(x+1)= 0 pull out the common factor and then stuck! I should have two answers such as 3x-1 which would actually be 3tan(t)-1, then I would take 3tan(t)=1 which gives me 3tan equals {1+h(2pi)}/3 and {pi-1m(2pi)}/3 I just can't figure this problem further, trig is tough for me =, this may be a the best website ever! thank you for your time Click here to see answer by Alan3354(34679)

 Question 672606: find the exact value of tan 27 degrees Click here to see answer by MathLover1(7480)

 Question 672584: Here is an example of a Trig function we are working on that I HAVE been able to solve, I think: solve trig equations algrebraically; sin^2(t)=2sin(t)+1 first set everything to zero; sin^2(t)-2sin(t)-1=0 then in this case I can use the foil method; (sin(t)-1)(sin(t)-1=0 then solve for (t); t=4.7+l(2pi) and t=pi-4.7i(2pi) This may seem like a more simple equation but....I'm just not sure about it still. Please help me solve: sec(t) = tan(t) I know to set everything equal to zero. sec(t)-tan(t)=0 I know sec=1/cos, but not sure if that would apply here.... thank you for your time Click here to see answer by Alan3354(34679)

 Question 671020: Find all solutions of this equation tan x = square root 3 Click here to see answer by lwsshak3(7679)

 Question 670973: An equation is given. (Enter your answers as a comma-separated list. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) sin θ/2− 1 = 0 Click here to see answer by lwsshak3(7679)

 Question 670962: An equation is given. (Enter your answers as a comma-separated list. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)csc θ − cot θ = sin θ Click here to see answer by lwsshak3(7679)

 Question 670902: what is the amplitude and period for y=5-(cosx/3)? Click here to see answer by lwsshak3(7679)

 Question 670629: (1 + sin x + cos x)^2 = 2(1 + sin x)(1 + cos x) How do I solve one side of this equation? Click here to see answer by lwsshak3(7679)

 Question 672645: Use the given information to find cos(x/2), sin(x/2), and tan(x/2): tan x = 2, pi < x < 3pi/2 Here is my solution, but I don't know how to get sin(x/2) and tan(x/2): 1 + (2)^2 = sec^2x 5 = sec^2x sec x = -sqrt(5) cos x = -1 / sqrt(5) = -sqrt(5)/5 cos^2(x/2) = 1/2(1+(-sqrt(5)/5)) = 5-(sqrt(5)/10) cos(x/2) = -sqrt(5-sqrt(5)/10) sin^2(x/2) = 1/2(1-(-sqrt(5)/5)) = 5+(sqrt(5)/10) sin(x/2) = ? tan(x/2) = ? Click here to see answer by lwsshak3(7679)

 Question 672742: How is cos pi/4 + cos pi/6 different than cos (pi/4 + pi/6)? Wouldn't the second one distribute giving you the same answer? Click here to see answer by fcabanski(1133)

 Question 672828: Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. Round your answers to three decimal places where appropriate.) sin 2θ + sin θ = 0 Click here to see answer by Alan3354(34679)

 Question 672918: if your distance from the foot of the tower is 20m and the angle of elevation is 40 degrees, find the height of the tower? Click here to see answer by jim_thompson5910(29613)

 Question 673626: what is the point (x,y) on the unit circle that corresponds to a real number 23pi/6 ? Click here to see answer by lwsshak3(7679)

 Question 673526: Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) cos 2θ = cos^2 θ − 1/2 θ = Click here to see answer by lwsshak3(7679)

 Question 673022: Find all t in the interval [0, 2π] satisfying (cos t)2 + 4 cos t + 3 = 0. Click here to see answer by lwsshak3(7679)

 Question 674149: the wheel of a bicycle has a diameter of 26 inches find the radian angle that the wheel turns when the bicycle turns 15 ft. for the answer i got 11pi/10 or 2.2 turns not sure if correct Click here to see answer by lwsshak3(7679)

 Question 674034: Using the fundamental identities to get an equivalent expression involving only sines and cosines, and then simplify it. cos(x) csc(x) I'm not to sure on how the answer is cot(x). I've tried replacing cos(x) as 1/sec(x) and csc(x) as 1/sin(x) then multiplied so each has the same denominator of sec(x)sin(x). Please explain on how the answer is cot(x). Click here to see answer by lwsshak3(7679)